Question

Use the following information to answer the next two questions: Harold needs to grow the $3,160 he currently has to $12,640 in seven years. He has found an investment that offers quarterly compounding and an effective annual rate (EAR) of 20%.

What is the periodic interest rate? (Remember a periodic interest rate is defined as: A P R m)

How long will it take to achieve the desired future value amount if this investment is made? Will he reach his goal in time at the specified interest rate?

Answer 1

Effective Annual Return (EAR) = (1+(APR/Number of Times Compounded))^Number of Times Compounded -1

.20 = (1+(APR/4))^4 -1

1+(APR/4))^4 = 1.20

1+(APR/4) = 1.20^(1/4)

= 1.04663513939

APR/4 = 1.04663513939-1

= 0.04663513939

APR = 0.04663513939*4

= 0.18654055756

APR = 18.65%

periodic interest rate = APR/Number of Times Compounded

= 18.65/4

= 4.6625%

Future value = Present value * (1+ (APR/no. of compounding ))^ (no. of periods*no. of compounding)

12640 = 3160*1.046625^4n

1.046625^4n = 12640/3160

= 4

4n = log4 / log1.046625

= 0.60205999132/0.01979110421

= 30.4207377684

n = 30.4207377684/4

= 7.61 years

It take 7.61 years to achieve the desired future value amount if this investment is made and he  Will not reach his goal in time at the specified interest rate