Question

How much money must you deposit into a savings account at the end of each year at 5% interest compounded annually in order to earn $13,157.13 interest during a 15-year period?

Please show your work and an explanation for your answer. Thank you!

Answer 1

Let the required annual deposit amount be $ K. This implies that the first deposit of $ K comes in at the end of Year 1 and is compounded for 14 years, the second deposit of $ K comes in at the end of Year 2 and is compounded for 13 years and so on.

Interest Rate = 5 % per annum compounded annually and deposit duration is 15 years.

Further, the interest to be earned is $ 13157.13 approximately which would be the difference between the final investment value and the total of the 15-year-end deposits of $ K each.

Final Investment Value = K x (1.05)^(14) + K x (1.05)^(13) + K x (1.05)^(12) + K x (1.05)^(11) + K x (1.05)^(10) + ...............+ K = K x [(1.05)^(15) - 1] / [1.05 - 1] = 21.5786 K

Total Value of Deposits = K x 15

Interest Earned = 21.5786 K - 15 K = 13157.13

K = $ 2000.00043 approximately.