Question

1. To save for college, parents of a newborn child invest $12,000 in a mutual fund at 10% interest, compounded semiannually, how much money will be in the account when the child is 18 years old? Round to the nearest cent.

2. Find out how long it takes a $2500 investment to double if it is invested at 7% compounded quarterly. Round to the nearest tenth of a year.

Answer 1

The formula for computing the maturity value F , where an initial investment P is placed at a rate of interest r, compounded semiannually, is F = P(1+r/200)^2t, where t is the number of years. Here, P = $ 12000, r = 10 and t = 18. Hence, F = 12000(1+10/200)^2*18 = 12000(1.05)³⁶ = 12000*5.791816136 = $ 69501.79( on rounding off to the nearest cent).

2. Let the $2500 investment double in t years when invested at 7% compounded quarterly. Then 5000 = 2500(1+7/400)^4t or, 2 = (1.0175)^4t . Now, on taking log of both the sides, we get 4t log (1.0175) = log 2 so that t = log 2/4log(1.0175) = 0.301029995/4*0.007534417897 =0.301029995/0.030137671 = 9.988495627 = 10 years ( on rounding off to the nearest tenth of a year). Thus, it will take 10 years for the investment to double.