Question

If your opportunity cost of capital is 12%. What is the future value of $500 in 5 years if it

is compounded:

a. Annually

b. Semi-annually

c. Quarterly

d. Monthly

Why is there a difference in the balances between the investment compounded quarterly

to the one compounded annually?

Answer 1

cost of capital = 12%

Present value = PV = 500

Time = 5 years

Annually

annual rate = r = 12%

number of periods = n = 5

Future value is calculated using the formula:

FV = PV*(1+r)^n

Therefore, FV = 500*(1.12)^5 = 881.1708

Semi-annualy

annual rate = 12%, semi-annual rate = r = 12%/2 = 6%

number of semi-annual periods = n = 5*2 = 10

FV = PV*(1+r)^n = 500*(1.06)^(10) = 895.4238

Quarterly

annual rate = 12%, qyarterly rate = r = 12%/4 = 3%

number of semi-annual periods = n = 5*4 = 20

FV = PV*(1+r)^n = 500*(1.03)^(20) = 903.0556

Monthly

annual rate = 12%, monthly rate = r = 12%/12 = 1%

number of semi-annual periods = n = 5*12 = 60

FV = PV*(1+r)^n = 500*(1.01)^(60) = 908.3483

Answer part 1

Compounded	FV
Yearly	881.1708416
Semi-annualy	895.4238483
Quarterly	903.0556173
Monthly	908.3483493

Part 2

The difference in the balances between the investment compounded quarterly to the one compounded annually is

903.0556173 - 881.1708416 = 21.8847757347064

Answer part 2: 21.8847757347064