Question

You decide to contribute to a mutual fund that averages 3.7% return per year. If you contribute $450 quarterly. Round all answers to the nearest cent as needed. a) How much will be in the account after 25 years? $ b) How much of this money did you deposit? $ c) How much of this money is interest earned? $

Answer 1

a). The formula for computing the future value (A) of an annuity is A = P[(1+r)ⁿ-1]/r where P is the periodic payment, r is the interest rate per period and nis the no. of periods. Here, P = $ 450, r = 3.7/400 = 37/4000 and n = 25*4 = 100. Then A = [450/(37/4000)][(1+37/4000)¹⁰⁰-1] = (1800000/37)*1.51116823 = $ 73516.29( on rounding off to the nearest cent) . Thus, there will be $ 73516.29 in the account after 25 years.

b). The money deposited is $ 450*25*4 = $ 45000. The amount of interest earned is $ 73516.29- $ 45000 = $ 28516.29.