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Time Value of Money
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* the concept that money you have now
is worth more than the identical sum in
the future due to its potential earning
capacity
Time Value of Money
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Future Value of Money
- the value of a current asset at a future
date based on an assumed rate of growth.
Present value (PV)
- is the current value of a future sum of money or
stream of cash flows given a specified rate of return.
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“ A Money you receives today is worth more 3
than a money received tomorrow, why?”
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E You need you need to sell your car and you
X receive offers from three different buyers.
• First offer: php 40,000 to be paid now
A • Second offer: php 41,000 to be paid one year
M from now
P • Third offer: php 46,000 to ne paid after 5
years
L Assume that the second and third offer has no
E credit risk, which offer would you accept?
Future Value of Money
the value of a current asset at a future date
based on an assumed rate of growth.
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INTEREST
Simple interest is computed based on the principal
amount (original amount) and based on the annual
time.
Simple Interest Computation
I = Prt
Where I = simple interest
P = principal
r = interest rate
t or n= time
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To find the future value (maturity value)
FV = P + I or FV = PV(1 + rt) or F = (1+ )n
To find the present value
P = (1+ )− or PV = FV / (1 + i)n
EXAMPLES: Future Value
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1. You invested Php 20,000.00 for three years at
5% simple interest rate. How much will you get after
three years?
FV = PV(1+ RT)
20,000((1+.05(3))
20,000(1+.15)
20,000(1.15)
FV= 23,000.00
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2. Alexpaid Php 1,537.50 with a loan
made 3 months before at 10% simple
interest. Find the principal amount of
the loan and the interest generated.
GIVEN: FV = 1,537.50 R=10% T= 3 months 3/12 = .25
P = FV / 1+RT I = FV – PV
1,537.50 / 1+.025 1,537.50 – 1,500.00
1,537.5 / 1.025 37.50
1,500.00
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3: The interest on a loan of Php
20,000.00 is Php 3,200.00. If the
rate is 8%, when is the loan due?
GIVEN: PV = 20,000.00 R = 8% I = 3,200.00
t = I / Pr
= 3,200.00 / 20,000(.08)
= 2 years
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4: Determine the simple interest rate if
an investment of Php 25,000.00
accumulates Php 27,625.00 in 18
months.
GIVEN: P = 25,000.00 FV = 27,625.00 t = 18 mos. Or 1.5 years
I = FV – PV r = I / PV(t)
= 27,625.00 – 25,000.00 = 2,625.00 / 25,000(1.5)
= 2,625.00 = .07 or 7%
EXAMPLES: Present Value
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What is the present value of receiving
P500 in three years, assuming a
discount rate of 8%?
GIVEN: fv = 500.00, t or n = 3 years, i = 8% 0.08/3 = .03
PV = FV / (1 + i)n PVIF = 1 / (1 + .08)з
= 500 (1 / 1+ .03)3 = 1 / 1.30
= 500 (.80) = 0.80
= 500(.80)
= 400
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EXAMPLES:
Linda would like to buy a car two years from now using the
proceeds of a 20% investment that is compounded semi-
annually. If the projected price of the car is ₱ 1,400,000, how
much money must be invested today to earn the price of the
car?
EXAMPLES:
You want to save for your child’s college
education and you estimate that you will
need P100,000 in 18 years. If you can earn
an annual interest rate of 5%, how much
money do you need to invest today?
PV = FV / (1+i)n
= 100,000 / (1 + .05 ) 18
= 100,000 / 2.4066
= 41,552
Or 40,000 to 50,000 of investment today
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EXAMPLES:
Linda would like to buy a car two years from now using the
proceeds of a 20% investment that is compounded semi-
annually. If the projected price of the car is ₱ 1,400,000, how
much money must be invested today to earn the price of the
car?
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