Question

A sum of money invested at 2% per 6-month period (semiannually will double in amount in approxi- mately how many years?

Answer 1

Answer: 17.5 years.

Explanation:

Assume that, Principal Amount = $1

n= number of semi annual periods which are unknown in our case.

i = interest rate = 2%

Future Value = 2 (Here, Future Value is said to be double the value of principal amount)

Future Value (F) = P (1+ i ) n

2 = 1 [1 + (2/100) ] n

2 = 1 [ 1 + 0.02 ] n

2 = 1 (1.02) n

2 = 1.02 n

n = log 2 / log 1.02

= .301 / 0.0086 = 35.

As the interest rate is calculated semi annually it will be calculated twice in every year. Thus when n= 35 times means that it will take 35/2 = 17.5 years to get the principal amount doubled.