5.
1- PV= $25,000
i= 8%
n= 10 years
Value of investment after 10 years= FV (year 10)
FV (year 10)= PVx(1+i¿n = $25,000x(1.08¿10
= $53,973.12
5.2- Amount invested today= PV= $7,500
i= 6%
N= 5 years
Value of investment after 5 years= FV (year 5)
FV (year 5)= PVx(1+i¿n = $7,500x(1.06¿5
= $10,036.69
5.3- PV= $5,000
i= 7.5%
n= 4 years
Frequency of compounding =2
Value of investment after 4 years= FV (year 4)
i mn 0.0075 2 x 4
FV (year 4)= PVx(1+ ¿ = $5,000x(1+ ¿
m 2
= $5,000x (1.0375¿8
= $6,712.35
5.4- PV= $2,000
i= 8.5%
n= 3years
Value of investment after 3 years= FV (year 3)
FV (year 3)= PVx(1+i¿n = $2,000x(1.085¿3
= $2,554.58
5.5- PV= $2,700
i= 5%
n= 4 years
m=2
Value of investment after 4 years= FV (year 4)
i mn 0.05 2 x 4
FV (year 4)= PVx(1+ ¿ = $2,700x(1+ ¿
m 2
= $2,700x (1.025¿8
= $3,289.69
5.2%
5.6-Effective quarterly rate= = 1.3%
4
Number of quarters in two years= 4x2=8
FV= 1000x(1+0.013¿8
= 1108.857
You can expect to earn 1108.857-1000= 108.857 in this period of time
5.7- a.Frequency of compounding = m= 4
Value of investment after 5 years
=FV5$154154.24=)021875.1(×100000=40875.0+1×100000=+1×=205×45mnmiPVFV
b.Frequency of compounding = m= 12 Value of investment after 5 years =
FV5$154637.37=)00729.1(×100000=120875.0+1×100000=+1×=605×125mnmiPVFV
c.Frequency of compounding = m= 365 Value of investment after 5 years =
FV5$154874.91=)00024.1(×100000=3650875.0+1×100000=+1×=18255×3655mnmiPVFV
d.Frequency of compounding = m= Continuous Value of investment after 5 years = FV
5.8- Growth Rate (g) = 12% every year. The total number of years remaining is 5.
Home runs R(1+g¿n
Where R= 15 (current rate of home runs hit)
G= 12% , n= 5 years
Home runs expected to be hit in 2019 are,
= 15 (1+.12)^5
= 26 (approximately)
5.9-
PV = FV / (1 + r)n
where, PV = Present value, FV = Future value, r = rate of interest, n = no. of years
PV = $25000 / (1 + 0.076)6 = $16,108.92
5.10- Future value = $750 (FV)
Number of years = 2 (n)
Interest rate = 6.5% (r)
Today investment (PV) = FV/(1+r)^n = 750/(1.065)^2 = $661.24
5.11-
Lending Value = $7,750 / (1 + 6%) ^ 3
= $7,750 / 1.1910
= $6,507.05
Maximum Amount You Willing To lend is $6,507.05.
5.12- FV = PV*(1 + r)^n
35000 = PV*(1+9.25/100)^5
PV = 22,488.5169
5.13- Face value of bond at maturity= FV (year 7)= $1,000
Appropriate discount rate= i= 4.5%
Number of years to maturity= n= 7 years
Present value of bond= PV
PV= FV = $ 1,000 = $734.83
¿¿ ¿¿
5.14- i= interest rate= 7%
n= the number of periods= 12 years
FV= future value of investment= FV (12 years) = $12,000
FV $ 12,000
PV= = = $5,328.14
¿¿ ¿¿
5.15- Borrowed amount = $1300
Interest rate offered by Bank = 6.5% annually (Assuming compounded annually)
Calculating the Value of loan along with Interest after 2 years:-
Loan Payable amount with Interest = Loan Amount(1+Interest rate)^2
= 1300(1+0.065)^2
= $ 1474.49
So, amount payable to Bank after 2 years is $1474.49
- Amount payable to Uncle after 2 years is $1500
Hence, it should be better to go with Bank rather than uncle. As, amount payable after 2 years to
Bank is less.
5.16- PV = 150
FV = 300
Rate = 9%
Rate = (FV/PV)1/n-1
9% = 21/n-1
21/n = 1.09
applying log on both sides
n = log(2)/Log(1.09) = 8.04 years
5.17- Year
Growth Rate
Number of Book Sold at Year end
Starting Year
53250
20%
53250 x (53250*20%) = 63900
First Year
63900
20%
63900 x (63900*20%) = 76680
Second Year
76680
20%
76680 x (76680*20%) = 92016
Third Year
92016
10%
92016 x (92016*10%) = 101217.6
Fourth Year
101217.6
5.18- Future value = Present value * (1 + R)^N
Let Last year sales = PV = $700,000
Expected annual growth in next 3 years = g1 = 20 %
Expected annual growth in next 2 years = g2 = 11 %
We have to find projected sales for last year.
Let projected sales of last year i.e year 5 = FV
FV5= PV (1+g)
= 700,000 (1.2)3 + 700,000 (1.11)2
= 700,000 * 1.728 + 700,000 * 1.232
= 1209600 + 862,400
= 2072,000
Therefore expected sales for Year 5 is $ 2072,000
5.19- We use the formula:
A=P(1+r/100)^n
Where
A=future value
P=present value
r=rate of interest
n=time period.
A=450*(1.25)^2*(1.21)*(1.18)
=450*2.2309375
=1004(Approx).
5.20- Principal amount (P) = $ 2500
a) 6.25 percent compounded semiannually for 12 years
= p*(1+rate/2)^2*n = 2500*(1+6.25%/2)^ 12*2 = $ 5,232.08
b) 7.63 percent compounded quarterly for 6 years
= P*(1+ rate/4)^6*4 = 2500*(1+ 7.63%/4)^ 24 = $ 3,934.48
c) 8.9 percent compounded monthly for 10 years
= P*(1+ rate/12)^12* 10 = 2500*(1+ 8.9%/12)^120 = $ 6,067.86
d) 10 percent compounded daily for 3 years
= P*(1+ rate/365)^365*3 = 2500*(1+ 10%/365)^365*3 = $ 3,374.51
5.21- a. Tenure = 5 year
Discount rate = 8.9%
Interest is compounding monthly. So present value is calculated below:
Present value = $3,500 / (1 + 8.9% / 12) ^ (5 × 12)
= $73,511 / 1.5579
= $2,246.57
Present value of amount receives after 5 years is $2,246.57.
b. Tenure = 8 year
Discount rate = 6.6%
Interest is compounding Quarterly. So present value is calculated below:
Present value = $3,500 / (1 + 6.6% / 4) ^ (8 × 4)
= $73,511 / 1.6882
= $2,073.16
Present value of amount receives after 8 years is $2,073.16.
c. Tenure = 4 year
Discount rate = 4.3%
Interest is compounding monthly. So present value is calculated below:
Present value = $3,500 / (1 + 4.3% / 365) ^ (4 × 365)
= $73,511 / 1.1877
= $2,946.96
Present value of amount receives after 5 years is $2,946.93
d. Tenure= 3 years
Annual interest rate= 5.7%
Then total payment he has to make after 3- year month at continuous is calculated below:
Future value 3,500
Present value= = = $2,949.93
en 2.7183
5.22- (a) 4.2 % compounded daily. Daily compounding rate = 4.2 / 365 = 0.01151 %
Number of Days in three years = 3 x 365 = 1095 days
Let the initial investment be M
Therefore, M = 5500 / (1.0001151)^(1095) = $ 4848.75
b- 4.9 % compounded monthly.
Monthly Compounding Rate = (4.9 / 12) = 0.4083 %
Number of months in three years = 12 x 3 = 36 months
Let the intial investment be $ M
Therefore, M = 5500 / (1.004083)^(36) = $ 4749.59
c- 5.2 % compounded quarterly
Quarterly Compounding Rate = (5.2/4) = 1.3 %
Number of Quarters in three years = 4 x 3 = 12 years
Let the initial investment be $ M
Therefore, M = 5500 / (1.013)^(12) = $ 4710.31
d- 5.4 % compounded annually
Let the initial investment be $ M
Therefore, M = 5500 / (1.054)^(3) = $ 4697.22
As the initial investment for the fourth option is the lowest, Samantha will go with the fourth
option.
5.23- Present value = 1.125 million
Future value = 2 * 1.125 = 2.25 million
Number of years = 11
5.24- Computation of Time required to make investment of $850 to $1000
Future Value = Present Value * (1+r)^n
$1000 = $850 * (1+0.05)^n
(1.05^n) = 1.17647
at n = 3.33 years 1.05^n will be equal to 1.17647
Thus Time required = 3.33 years
5.31- Amount Invested = $2,500
Amount received after 3 years = $3,700
Return on Investment = (Amount received / Amount invested)^(1/n) - 1
Return on Investment = ($3,700 / $2,500)^(1/3) - 1
ROI= 1.48^(1/3) - 1
ROI = 1.1396 - 1
ROI = 0.1396
ROI = 13.96%
5.32- We know that FV = PV*(1+I)^N
Puting values, we get
4800 = 2400 *(1+I)^4
Solving, we get
(1+I)^4 = 4800/2400 = 2
Taking Log of both sides, we get
4 Log(1+I) = Log2 = 0.3010
ie Log(1+I) = 0.3010/4 = 0.0753
Taking Antilog, we get
1+I = 1.1892
ie I = 1.1892-1 = 0.1892 = 18.92%
5.34- Interest)^6 * (1 + Next 3 years Interest)^3
Balance in account at the end of year 16 = 5000 * (1 + 7.30%)^7 * (1 + 5.50%)^6 * (1 +
8.20%)^3
Balance in account at the end of year 16 = 5000 * 1.6376 * 1.3788 * 1.2667
Balance in account at the end of year 16 = $14300.94
b. Balance in account at the end of year 21 = investment * (1 + First 7 Year Interest)^7 * (1 +
next 6 Year Interest)^6 * (1 + Next 3 years Interest)^3 * (1 + next 2 years interest)^2 * (1 + last 3
years interest)^3
Balance in account at the end of year 21 = 5000 * (1 + 7.30%)^7 * (1 + 5.50%)^6 * (1 +
8.20%)^3 * (1 + 4.60%)^2 * (1 + 7.60%)^3
Balance in account at the end of year 21 = 5000 * 1.6376 * 1.3788 * 1.2667 * 1.1444 * 1.1578
Balance in account at the end of year 21 = $18948.91
c. Balance Now if additional deposit made = $18948.91 + Additional deposit * (1 + First 6 Year
Interest)^6 * (1 + Next 3 years Interest)^3 * (1 + next 2 years interest)^2 * (1 + last 3 years
interest)^3
Balance Now if additional deposit made = $18948.91 + 1200 * (1 + 5.50%)^6 * (1 + 8.20%)^3 *
(1 + 4.60%)^2 * (1 + 7.60%)^3
Balance Now if additional deposit made = $18948.91 + 1200 * 1.3788 * 1.2667 * 1.1444 *
1.1578
Balance Now if additional deposit made = $18948.91 + 2777.14
Balance Now if additional deposit made = $21726.05
