Personal Finance

Practice Final Exam (Solutions)

Section I. Multiple Choice

Please circle the correct answer for each of the following questions. Note that there is
only one correct answer for each question. Each question is worth 2 points.

1. Which of the following statements is true about the balance of a single deposit in an
interest earning savings account? (Only one is true.)

A) The balance will not grow exponentially because multiple deposits are required
to achieve exponential growth.

B) The balance will grow exponentially, but only if the interest rate increases so that
the dollar amount of interest earned increases.

C) The balance will grow exponentially, but only if the interest rate is high enough.

D) If the balance doubles after 15 years, it will more than triple after 30 years
because of compound interest.

Answer: D

A is false. Multiple deposits are not required to achieve exponential growth. Any
balance earning interest will grow exponentially because of compound interest.

B is false. Even if the interest rate remains constant, the balance will grow
exponentially because of compound interest.

C is false. As long as the interest rate is above zero, the balance will grow
exponentially. The higher the interest rate, however, the faster it will grow.

D is true. If a balance doubles after 15 years, it will double again after another 15 years.
In total, after 30 years, a balance will quadruple.

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2. Which of the following about Perkins loans is false? (Only one is false)

A) No interest accrues on the loan while a student is in school, and repayment does
not begin immediately after a student graduates, but following a grace period
after graduation.

B) The effect of subsidized interest and the grace period is that the implicit interest
rate on the loan decreases below the stated APR.

C) If a Perkins loan did not have a grace period, but no interest accrued and no
payments were due while the student is in school, the implicit rate on the loan
would be equal to the stated APR.

D) If interest on a Perkins loan did accrue while the student is in school and
throughout the grace period, but no payments were required while the student is
in school or through the 9-month the grace period, the implicit interest rate on the
loan would be equal to the stated APR.

Answer: C

A is true. A Perkins loan is a federal student loan with subsidized interest and an
additional 9-month grace period.

B is true. By allowing the student to push payments further into the future without
accruing any interest, the implicit interest rate on the loan decreases below the stated
APR.

C is false. If the student is able to push payments until graduation day without accruing
interest, the implicit interest rate on the loan decreases below the stated APR (but not
by as much as it would if they were also able to further delay payment for an additional
9 months).

D is true. Although the student would be able to defer payment in this instance, they
would be charged interest for doing so, and so the implicit interest rate on the loan
would be equal to the stated APR.

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3. Which of the following is true of the amortization of an installment loan with monthly
payments? (Only one is true.)

A) The monthly payment increases over time.

B) The principal portion of the monthly payment decreases over time.

C) The interest portion of the monthly payment increases over time.

D) The interest portion of the monthly payment decreases over time.

Answer: D

A is false. The monthly payment on an installment loan remains constant over the life of
the loan.

B and C are false and D is true. Each month, a portion of the payment reduces the loan
principal. As the principal decreases, the interest due at the end of each period
decreases, so C is false and D is true. Because the payments are fixed, lower interest
payments implies that a greater share of the payment is going to principle, so B is false.

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4. Which of the following statements about mortgage refinancing is true? (Only one is
true.)

A) Refinancing is always a bad idea because of the large closing costs.

B) If the interest rate has dropped by at least 0.25%, refinancing is always a good
deal because the lower future monthly payments will make up for all other costs.

C) With all other things being equal, refinancing a mortgage is more likely to be a
good deal if the borrower still has many years left on the mortgage and plans to
stay in the home for a long time after refinancing.

D) Refinancing is only a good deal if the borrower did not take any mortgage points
on the original mortgage but takes at least two points during the refinance.

Answer: C

A is false. If the savings from a reduced monthly payment outweigh the initial large
closing costs, refinancing is a good idea.

B is false. There are many factors to consider besides the drop in the interest rate on
the loan. For example, if the interest rate dropped by 0.25% but the homeowner sold
the home a couple of months later, the total of the monthly savings probably would not
outweigh the large initial closing costs of refinancing.

C is true. The longer a borrower stays in a home, the more monthly payments they
make. Therefore, the sum of the monthly savings from refinancing will be greater the
longer the borrower stays in the home, and the more likely it will be that the savings
outweigh the initial closing costs.

D is false. Refinancing can be a good deal regardless of whether the borrower took
points on their original mortgage and/or takes points on their refinancing mortgage.

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5. Which of the following statements is true? (Only one is true.)

A) It’s only a good idea to buy a stock if you believe you will be able to sell it to
somebody else at a higher price at a later date.

B) Generally, a stock issued by a company is safer than a bond because

stockowners may achieve very high returns if the company performs well, while
bondholders’ returns are limited by the coupon rate of the bond.

C) Mutual funds provide superior diversification benefits than index funds because,
in the U.S., index funds are legally required to only invest in the stocks of the
largest 100 companies.

D) Some studies find that mutual fund managers are not able to outperform the
market regularly after considering transaction costs. This evidence that supports
the efficient market hypothesis.

Answer: D

A is false. If a stock provides high enough dividends to justify its current price, it is a
good idea to buy a stock even if you’re not sure if you’ll be able to sell it at a gain in the
future.

B is false. Stocks are generally considered riskier than bonds. Even though they have
the potential for higher returns than bonds, they also have the potential for lower
returns.

C is false. Index funds in the U.S. are not required to invest only in the 100 largest
companies. For example, many companies provide S&P 500 index funds, which invest
in the 500 largest companies in the U.S.

D is true. The efficient market hypothesis states that it is excessively difficult to

consistently outperform the stock market after considering all opportunity or transaction
costs. The studies listed provide evidence that directly supports this claim.

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6. Which of the following statements about Social Security is true? (Only one is true)

A) Social Security is necessarily a bad deal because the return implied by Social
Security is usually lower than the historical return on stocks.

B) Collecting Social Security early is never a good idea because the drop in annual
benefits from collecting early outweighs the ability to collect a few extra years’
worth of benefits.

C) With all else being equal, Social Security benefits retirees with above-average
life expectancies more than retirees with average life expectancies.

D) Social Security is the best asset for retirees because it is not subject to financial
risk, longevity risk, inflation risk, or any other risk.

Answer: C

A is false. Though the returns implied by Social Security may tend to be lower than the
historical returns on stocks post hoc, Social Security benefits are not subject to the
same financial risks as stock, so a lower return does not make them necessarily inferior.

B is false. The extra years’ worth of benefits may outweigh the drop in annual benefits.
Further, because the extra benefits come earlier, they are more valuable because of the
time value of money.

C is true. The longer a retiree lives, the more years’ worth of benefits they will receive,
so retirees who live longer will receive more benefits.

D is false. Though Social Security is not subject to any of the listed risks, it is subject to
the political risk that the formula governing benefits may change over time. Further,
even though it is less risky than other assets, other assets may provide a higher return.

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7. Which of the following statements is false? (Only one is false)

A) A retiree may die before using all of his or her retirement funds. This is an
example of longevity risk.

B) Because stock prices fluctuate often, an investor may be forced to sell his or her
stock at a price lower than that at which it was purchased. This is an example of
financial risk.

C) Corporations below investment grade have a higher risk of defaulting on their

debt obligations than investment grade corporations. An investor that buys the
bond of such a company may not receive the contractual payments promised by
the bond in the event of such a default. This is an example of default risk.

D) If the cost of living increases faster than expected, a retiree may be unable to
purchase as much as he or she planned during retirement. This is an example of
inflation risk.

Answer: A

A is false. Longevity risk is the risk that a retiree will outlive his or her retirement funds,
not die before using all of his or her retirement funds.

B, C, and D are all true. Each statement defines the listed risk.

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8. Which of the following statements is false? (Only one is false.)

A) For a given change in interest rates, duration provides a better approximation for
the change in a bond’s price for a long-term bond than for a short-term bond.

B) The duration of a bond may be equal to its maturity.

C) For a given change in interest rates, the new price of a bond estimated using
duration will always underestimate the actual new price of the bond (calculated
by taking the present value of the cash flows).

D) The price of a longer-term bond is more sensitive to interest rate changes.

Answer: A

A is false. For long-term bonds, duration provides a less accurate estimate for a given
change interest rates.

B is true. The duration of a zero-coupon bond is its maturity.

C is true. See slides.

D is true. The duration for is larger for longer-term bonds, and duration measures a
bond’s sensitivity to interest rate changes. Therefore, long-term bonds are more
sensitive to interest rate changes.

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9. Which of the following statements is true? (Only one is true.)

A) An investor may reduce the standard deviation of the returns on his or her
portfolio by buying several shares of the same company’s stock.

B) An investor may completely eliminate financial risk in a U.S. stock portfolio by

diversifying across a sufficient number of stocks.

C) Risk diversification is only effective if two assets are positively correlated (i.e.
have a correlation coefficient of greater than zero).

D) If two asset classes are uncorrelated, the standard deviation of returns on a

portfolio weighted equally between these two assets will be less than it would be
if the two assets were perfectly, positively correlated.

Answer: D

A is false. To diversify, an investor must purchase different assets (that move

independently) not more of the same asset. Mathematically, since multiple shares of
the same stock are perfectly positively correlated, there is no diversification benefit to
purchasing several shares.

B is false. Because common factors affect all U.S. stocks, only a portion of the risk may
be eliminated by diversifying across multiple stocks. Systematic, or non-diversifiable,
risk will still remain.

C is false. The less positively correlated a two assets are, the greater the diversification
benefits. If assets are completely uncorrelated, for example, the diversification benefits
are strong. If assets are negatively correlated (which was not covered in the lectures),
diversification benefits are even stronger.

D is true. If two assets are uncorrelated, the standard deviation for any given mix
between the two assets will be less than it would be if they were perfectly positively
correlated.

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10. Which of the following statements is false? (Only one is false.)

A) With all else equal, an immediate life annuity is less expensive than a deferred
life annuity because of the time value of money.

B) A life annuity can be purchased to insure against longevity risk.

C) A variable annuity indexed to the performance of the stock market is subject to

financial risk, but a fixed annuity is not.

D) The implied return received on a fixed life annuity depends on how long the
annuitant (the purchaser of the annuity) lives.

Answer: A

A is false. An immediate life annuity is more expensive than a deferred life annuity
because the benefits are received earlier, so they are more valuable because of the
time value of money.

B is true. A life annuity pays benefits for as long as the beneficiary lives, so it can be
used to insure against the risk that a retiree may outlive their savings, which is longevity
risk.

C is true. If the benefits paid by an annuity are indexed to the stock market, they will
fluctuate up and down with the stock market, and so are subject to the same financial
risk as the stock market.

D is true. The longer an annuitant lives, the more benefits they will receive, and so the
higher their implied return from purchasing the annuity will be.

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Section II. Short Answer

Please write your answers to the following questions in the spaces provided. Please
show your work if you wish to receive partial credit. Each question is worth 3 points.

11. A worker is saving for a down payment on a house. If the down payment will be
$40,000 and she can earn 5% interest on her savings, how much must she set aside
today to make the down payment in 10 years?

Answer: $24,556

Using the interest rate formula:

!
𝐹 $40,000
𝐹 =𝑃 1+𝑟 →𝑃= !
= = $24,556
1+𝑟 1.05 !"

12. Max borrows $400 for two weeks from a local payday lender. His fee for borrowing
the $400 for two weeks is $56, which is due in two weeks along with the original $400.
What is the APR on this payday loan?

Answer: 364%

Given that there are 52 weeks in a year, the APR of the loan can be calculated as:

$56 52
𝐴𝑃𝑅 = ∗ = 364%
$400 2

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13. Amy recently graduated from college and has $12,000 in ten-year student loans
carrying a 6% APR. If she makes monthly payments of $200, how long will it take her to
pay down her balance?

Answer: 72 months (6 years)

Using a financial calculator:

Time Value of Money

P/Y 12
PV $12,000
PMT -$200
FV $0
I/Y 6%

N= 72

It will take 72 months, or 6 years.

14. A bond issued by Acme Inc. that pays quarterly coupons at a rate of 10% for the
next five years is currently selling at $1,100 per $1,000 par. Calculate the yield-to-
maturity of this issue.

Answer: 8.52%

Because the bond is selling at greater than $1,000 per $1,000 par, it is selling at a
premium.

The bond costs $1,100 today, will pay 20 quarterly coupons of (0.10*$1,000)/4 = $25,
and repay the $1,000 face value in five years (20 quarters). The implicit quarterly
interest rate paid by the bond is therefore:

Time Value of Money

P/Y 4
PV -$1,100
PMT $25
FV $1,000
N 20

I/Y= 7.76%

This is less than the 10% coupon rate because the bond sells at a premium.

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15. Last year, Acme Inc. paid dividends of $15 per share. Value the company using a
discount rate of 18% assuming that dividends grow by 3% per year.

Answer: $103

The value of each share of the company’s stock can be found by applying the Gordon
Growth Model:

𝐷! 1 + 𝑔 $15 1.03
𝑃! = = = $103
𝑟−𝑔 0.18 − 0.03

16. A man is saving for his daughter’s college education. He expects to earn an
average return of 6% on his investment account and will need $80,000 in 18 years. He
plans to meet this goal by setting aside the same amount at the beginning of each year
for the next 18 years. What amount must he set aside each year to meet this
commitment?

Answer: $2,442

The amount may be found using a financial calculator:

Time Value of Money

Mode BEG
P/Y 1
PV $0
FV $80,000
I/Y 6%
N 18

PMT= -$2,442

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17. This year, Rob spent $1,000 on a new suit. If inflation is 2.5% per year, how much
will it cost him to purchase the same suit in ten years? (Assume that the price change
of the suit is in line with inflation.)

Answer: $1,280.08

After ten years, the same suit will cost:

! !"
𝑃! = 𝑃! 1 + 𝑖 = $1,000 1.025 = $1,280.08

18. Today, Ryan takes out a 30-year, $240,000 mortgage with an APR of 6%. If
inflation is 2% over the term of the mortgage, what will be the approximate real interest
rate Ryan pays on the mortgage?

Answer: 4%

The real interest rate can be approximated as:

𝑟 ≈ 𝑛 − 𝑖 = 6% − 2% = 4%

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19. Amy and Joe both invest $6,000 in the stock market. Amy invests passively and
holds onto her stocks for 30 years. Joe actively trades, turning over his portfolio yearly.
Consequently, Amy is subjected to a deferred long-term capital gains tax of 15%, while
Joe is subject to an annual short-term capital gains tax at his marginal income tax rate,
which is 25%. If both earn an annual return of 7% on their investment, how much more
will money will Amy have in 30 years, after tax, compared to Joe?

Answer: $11,874

Because Amy invests for the long-term and is subject to a deferred capital gains tax of
15%, her final wealth will grow to:
! !"
𝐹 =𝑃∗ 1+𝑟 1 − 𝑇 + 𝑇 = $6,000 1.07 1 − 0.15 + 0.15 = $39,723

Because Joe trades actively and turns over his portfolio every year, he is subject to a
25% accrual tax:
! !"
𝐹 =𝑃 1+𝑟 1−𝑇 = $6,000 1 + .07 1 − 0.25 = $27,849

So Amy will have $39,723 − $27,849 = $11,874 more than Joe after 30 years.

20. Michael invests $40,000 in a start-up, $20,000 of which is borrowed at an interest

rate of 10%. If the project returns 14%, what is Michael’s return on equity?

Answer: 18%

Michael’s return on equity can be found as:

𝐷! $20,000
𝑅=𝑟+ 𝑟 − 𝑖 = 14% + 14% − 10% = 18%
𝐸! $20,000

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Section III. Long Answer

Please write your answers to the following questions in the spaces provided. Please
show your work if you wish to receive partial credit. Each question is worth 5 points.

21. Jack is considering opening a new restaurant. To do so would require an

investment of $120,000 today. He estimates that the restaurant would generate profits
of about $35,000 a year for the next six years.

For the following questions, assume all cash flows occur at the end of each year.

(a) Calculate the NPV of opening the restaurant using a discount rate of 18%.

NPV: $2,416

The NPV can be found using a financial calculator:

Cash Flow Worksheet

CF 0 -$120,000
C01 $35,000
F01 6
I 18%

NPV= $2,416.09

(b) Calculate the IRR of opening the restaurant.

IRR: 18.78%

The IRR may be found using a financial calculator:

Cash Flow Worksheet

CF 0 -$120,000
C01 $35,000
F01 6

IRR= 18.78%

(c) Assuming Jack requires a return of 20%, should he invest in the restaurant?

No. Because the IRR of 18.78% does not exceed Jack’s 20% required return, he
should not invest in the restaurant.

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22. Janice has a $2,000 balance on a credit card with a 18% APR, on which she
usually just makes the minimum monthly payment of $30.

For the following questions, assume no additional borrowing.

(a) If Janice doubles the minimum monthly payment and makes payments of $60 per
month, how long it take for Janice to pay off her credit card?

Months to pay off credit card: 46.6 months

This can be found using a financial calculator:

Time Value of Money

P/Y 12
PV $2,000
PMT -$60
FV $0
I/Y 18%

N= 46.6

(b) If Janice wants to completely pay off her credit card in two years, how much should
her monthly payment be each month?

Monthly payment: $99.85

Using a financial calculator:

Time Value of Money

P/Y 12
PV $2,000
FV $0
I/Y 18%
N 24

PMT= -$99.85

(c) Instead, if Janice continues to make the minimum monthly payment of $30 for the
next two years, will her balance be less than the $2,000 balance she started with?

No. If Janice makes only the minimum monthly payment of $30, she will only be paying
interest, so her balance will not decline.

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23. Ann and Andy are looking for a new home and find a $300,000 house that they like.
Their bank offers them a 30-year mortgage at an 8% APR with a 20% down payment
and no points. But if Ann and Andy are willing to pay two points, their bank will drop the
APR on the mortgage to 7.5% points. They expect they will stay in the home for at least
six years.

(a) If they take the points, what will the outstanding balance on their mortgage after six
years?

Balance: $227,082

After their 20% down payment, they must borrow $240,000. Their monthly payment will
be $1,678.11. After 5 years (60 months), their mortgage balance will be $227,082.

Time Value of Money

P/Y 12
PV $240,000
FV $0
I/Y 7.5%
N 360

PMT= -$1,678.11
N 72

FV= -$223,866.58

(b) Assuming they take the points and stay in the home for six years, calculate the
implicit APR on the mortgage with two points?

Implicit APR: 7.93%

If Ann and Andy take the points, they must pay 0.02*$240,000 = $4,800 up front.
Because they receive $240,000 for the loan, but must immediately pay the bank $4,800,
they only receive $235,200 on net. Using the monthly payment and ending balance
found in part (a) above, the implied APR can be found using a financial calculator:

Time Value of Money

P/Y 12
PV $235,200.00
PMT -$1,678.11
FV -$223,866.58
N 72

I/Y 7.93%

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(c) Should they take the points? Yes. The 7.93% implied APR with points is less than
the 8.0% APR without points.

24. Caitlin is helping her parents plan for retirement. Her mother and father plan to
retire in 25 years at age 65, but have only accumulated $100,000 of savings. The
couple can earn an interest rate of 6% on their investment account while saving for
retirement, but plan to move funds into a safer mix of assets that will yield 3% when
they reach retirement. The couple wishes save enough to maintain withdrawals of
$40,000 per year for 40 years after they retire.

For the following questions, assume zero inflation and that all cash flows occur at the
end of the year.

(a) How much must Caitlin’s parents set aside each year until retirement to meet their
goal?

Annual contribution: $9,029.59

To sustain withdrawals of $40,000 per year for 40 years in retirement while earning an
annual return of 3%, Caitlin’s parents must have $924,591 when they retire:

Time Value of Money

P/Y 1
PMT $40,000
FV $0
I/Y 3%
N 40

PV= -$924,590.88

And to reach this level of savings in the next 25 years while earning an annual return of
6% on their assets, given that they already have $100,000 saved, they must save
$9,029.59 per year:

Time Value of Money

P/Y 1
PV -$100,000
FV $924,591
I/Y 6%
N 25

PMT= -$9,029.59

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(b) If Caitlin’s parents make the annual contributions found in part (a) and realize their
assumed return of 6%, how much will they have in their retirement account at
retirement?

Balance at retirement: $924,591 (See the solution to part a)

(c) Statistically, Caitlin’s parents don’t expect to live for 40 years after retirement, but
they might. By saving enough to last them 40 years in retirement, Caitlin’s parents are
insuring themselves against what risk?

Risk: Longevity Risk

Longevity risk is the risk that a retiree might outlive their savings. By saving enough to
last longer than they expect to live, Caitlin’s parents are insuring against this risk.

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