Question

Calculate the presentvalue of $5,000 received five years from today if your investments pay a. 6 percent compounded annually b. 8 percent compounded annually c. 10 percent compounded annually d. 10 percent compounded semiannually e. 10 percent compounded quarterly.

Answer 1

Given:

Amount = $5000

Tenure = 5 years.

Future value =
`Present value* (1+r)^(n)`

where

n is number of periods

r is rate per period.

(a) 6% compounded annually.

Interest is compounded annually

No of periods in 5 years = 5

Future value = 5000
`(1+0.06)^(5)` = 5000 × 1.33823 = $6691.15

(b) 8% compounded annually

Interest is compounded annually

No of periods in 5 years = 5

Future value =5000
`(1+0.08)^(5)` = 5000×1.46933 = 7346.65

(c) 10% compounded annually

Interest is compounded annually

No of periods in 5 years = 5

Future value = 5000
`(1+0.10)^(5)` = 5000×1.61051 = $8052.55

(d) 10% compounded semiannually

Interest is compounded semiannually

No of periods in 5 years is 5*2 = 10

Rate per period = 10÷2 = 5%

Future value =5000
`(1+0.05)^(10)` = 5000×1.62889 = $8144.45

(e) 10% compounded quarterly

Interest is compounded annually

∴No of periods in 5 years = 5×4 = 20

Rate per period = 10÷4 = 2.5

Future value = 5000
`(1+0.025)^(20)` = 5000×1.63862 = $8193.10