Question

4. Determine the value at the end of four years of a $5,000 investment today that pays a nominal annual interest rate of 15%, compounded:

a)Annually

b)Semiannually

c)Quarterly

d)Monthly

Answer 1

(a)

Invested amount (PV) = $5,000

Interest rate = 15% compounded annually

Time period = 4 years

Calculate the value at the end of four years -

Value = PV(1+r)ⁿ

Value = $5,000(1+0.15)⁴

Value = $5,000 * 1.7490 = $8,745

The value at the end of four years is $8,745

(b)

Amount invested (PV) = $5,000

Interest rate = 15% compounded semiannually

Since, interest is compounded semiannually, interest rate has to be divided by 2

Adjusted interest rate = 15/2 = 7.5% or 0.075

Time period has to be multiplied by 2.

Adjusted time period = 4 * 2 = 8

Calculate the value at the end of four years -

Value = PV(1+r)ⁿ

Value = $5,000(1+0.075)⁸

Value = $5,000 * 1.7835 = $8,917.5

The value at the end of four years is $8,917.5

(c)

Amount invested (PV) = $5,000

Interest rate = 15% compounded Quarterly

Since, interest is compounded quarterly, interest rate has to be divided by 4

Adjusted interest rate = 15/4 = 0.0375

Time period has to be multiplied by 4.

Adjusted time period = 4 * 4 = 16

Calculate the value at the end of four years -

Value = PV(1+r)ⁿ

Value = $5,000(1+0.0375)¹⁶

Value = $5,000 * 1.8022 = $9,011

The value at the end of four years is $9,011.

(d)

Amount invested (PV) = $5,000

Interest rate = 15% compounded monthly

Since, interest is compounded monthly, interest rate has to be divided by 12

Adjusted interest rate = 15/12 = 0.0125

Time period has to be multiplied by 12

Adjusted time period = 4 * 12 = 48

Calculate the value at the end of four years -

Value = PV(1+r)ⁿ

Value = $5,000(1+0.0125)⁴⁸

Value = $5,000 * 1.8153 = $9,076.5

The value at the end of four years is $9,076.5