Question

18-a) What would be the future value of $18,000 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and interest on the investment is compounded semi-annually?

b) How would your answer for (a) change if quarterly compounding were used?

Answer 1

18.a. The future value is computed as shown below:

Future value = Present value (1 + r)ⁿ

r is computed as follows:

= 18% / 2 (Since the interest is compounded semi annually, hence divided by 2)

= 9% or 0.09

n is computed as follows:

= 8 x 2 (Since the interest is compounded semi annually, hence multiplied by 2)

= 16

So, the amount will be computed as follows:

= $ 18,000 x 1.09¹⁶

= $ 71,465.51 Approximately

18.b. The future value is computed as shown below:

Future value = Present value (1 + r)ⁿ

r is computed as follows:

= 18% / 4 (Since the interest is compounded quarterly, hence divided by 4)

= 4.5% or 0.045

n is computed as follows:

= 8 x 4 (Since the interest is compounded quarterly, hence multiplied by 4)

= 32

So, the amount will be computed as follows:

= $ 18,000 x 1.045³²

= $ 73,619.66 Approximately

Feel free to ask in case of any query relating to this question