Question

You just received a bonus of ?$1000.

a. Calculate the future value of ?$1000?, given that it will be held in the bank for 8 years and earn an annual interest rate of 7 percent. What is the future value of ?$1000 in a bank account for 8 years at an annual interest rate of 7 ?percent? $________?(Round to the nearest? cent.)

b. Recalculate part ?(a?) using a compounding period that is? (1) semiannual and? (2) bimonthly.

c. Recalculate parts ?(a?) and ?(b?) using an annual interest rate of 14 percent.

d. Recalculate part ?(a?) using a time horizon of 16 years at an annual interest rate of 7 percent.

e. What conclusions can you draw when you compare the answers in parts ?(c?) and ?(d?) with the answers in parts ?(a?) and ?(b?)?

Answer 1

For solving these questions, we simply need to use the basic time value of money function:

FV = PV * (1 + r)ⁿ

a) PV = $1000, n = 8 years, r = 7%

FV = 1000 * (1 + 7%)⁸

^{FV = $1,718.2}

b) For semi-annual compounding, n = 2 * 8 = 16 semi-annual periods, r = 7%/2 = 3.5% semi-annually

FV = $1000 * (1 + 3.5%)¹⁶

FV = $1,734.0

For bimonthly compounding, n = 48 bimonth periods, r = 7%/6

FV = $1000 * (1 + 7%/6)⁴⁸

FV = $1,745

c. Annual Interest Rate = 14%

Annual compounding: FV = 1000 * (1 + 14%)⁸ = $2,852.6

Semi-Annual compounding: FV = 1000 * (1 + 7%)¹⁶ = $2,952.2

Bi-monthly compounding: FV = 1000 * (1 + 14%/6)⁴⁸ = $3,025.7

d. n = 16 years

Annual compounding: FV = 1000 * (1 + 7%)¹⁶ = $2,952.2

Semi-Annual compounding: FV = 1000 * (1 + 3.5%)³² = $3,006.7

Bi-monthly compounding: FV = 1000 * (1 + 7%/6)⁹⁶ = $3,045.0

e. Looking at the answers in part c and d and comparing them with those in part a and b, we can draw three conclusions:

- Higher the frequency of compounding, higher is the future value of money for same interest rate and time period

- Higher the interest rate, higher is the future vale

- Longer the time invested, higher is the future value