Question

3. Determine the value at the end of nine years of a $12,500 investment today that pays a nominal annual interest rate of 15%, compounded: a) Annually b) Semiannually c) Quarterly d) Monthly

Answer 1

a)

Future value

= Present Value x ( 1 + Rate of interest ) ^ Number of periods

Where,

Present Value = $12,500

Rate of interest = 15% or 0.15

Number of periods = 9

So, Future Value = $12,500 x (1.15 ^ 9)

= $12,500 x 3.517876

= $ 43,973.45

b)

When interest is compounded semi-annually, interest rate is divided by 2 and time period is multiplied by 2

So, Rate of interest = 15 / 2 = 7.5% or 0.075

Number of periods = 9 x 2 = 18

So, Future Value

= $12,500 x ( 1.075 ^ 18)

= $12,500 x 3.675804

= $ 45,947.55

c)

When interest is compounded quarterly, interest rate is divided by 4 and time period is multiplied by 4

So, Rate of interest = 15 / 4 = 3.75% or 0.0375

Number of periods = 9 x 4 = 36

So, Future Value

= $12,500 x ( 1.0375 ^ 36)

= $12,500 x 3.763326

= $ 47,041.58

d)

When interest is compounded monthly, interest rate is divided by 12 and time period is multiplied by 12

So, Rate of interest = 15 / 12 = 1.25% or 0.0125

Number of periods = 9 x 12 = 108

So, Future Value

= $12,500 x ( 1.0125 ^ 108 )

= $12,500 x 3.825282

= $ 47,816.03