Gillian has 10000 to invest in a mutual fund The average ann

Gillian has $10000 to invest in a mutual fund. The average annual rate of return for the past five years was12.25% compounded annually. assuming this rate, determine how long it will take for her investment to double.

Solution

The formula for compound interest is F = P( 1 + r)ⁿ where P is the principal or the initial amount, F is the future value, r is the rate of interest in decimals and n is the number of intervals. Let us assume that the amount doubles in n years. Thus, we have P = $ 10000, F = $ 2 *10000 = $ 20000, r = 12.25/100 = 0.1225. Then 20000 = 10000( 1 + 0.1225)ⁿ or, (1.1225)ⁿ = 20000/10000 = 2. Taking logarithms of both the sides, we have n log 1.1225 = log 2 so that n = log 2/ log 1.1225 = 0.301029995/0.050186349 = 5.998244562 years or, say 6 years ( on rounding off). Thus it will take 6 years for Gillian\'s investment to double.