All the Years of Her Life

by Morley Callaghan

Start Free Trial

To what sum will $2000 amount to in 10 years if invested at a 4% effective annual rate for the first 5 years and than at a rate of 6% compounded semiannually thereafter?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The first five years are very straightforward. The value of the money increases by 4 percent every year. The math behind that is simple - each year you multiply the initial value by 1.04, or to find the final result of that period of time, you multiply the initial 2000 by 1.04^5, because the interest compounds 5 times. Therefore, after five years, the money will be worth approximately $2433.

The second half is a bit more tricky. Semiannual interest means that half the overall value of interest is compounded twice a year. So, 6% interest would mean that the value increases by 3% every six months. To find the overall value of the money after this period, you would multiply the initial value by 1.03^10, since half of the 6% interest compounds ten times over 5 years. Therefore, after 10 years, the money is worth $3270.16, or a 63.5% overall increase.

Approved by eNotes Editorial Team