You’ve been given $25,000 for your 21st birthday! You decide the prudent thing to do is control your inclination to spend it now, and instead you lock it into an investment that will earn you 8% inte

Question

You’ve been given $25,000 for your 21st birthday! You decide the prudent thing to do is control your inclination to spend it now, and instead you lock it into an investment that will earn you 8% interest for ten years, figuring you’ll probably need the money then more than you do now. What will the $25,000 be worth 10 years from now? (Before you answer, though, do you expect the final number to bigger or smaller than $25,000? Why?)

Answer 1

Hey Anna!

This question is testing your knowledge on the concept of compounding interest (the ability to earn interest on interest). For example, If you were to invest $25,000 and receive a return of 8% during the first year, your balance at the end of year 1 would be: $25,000 x (1+(8/100)) or $25,000 x 1.08 = $27,000.

Then, in year 2, you would earn 8% interest on your balance of $27,000. Your new balance at the end of year two would be equal to $27,000 * 1.08 = $29,160. The process would then continue for the remainder of the 10 year period.

Year 1: $25,000 * 1.08 = $27,000

Year 2: $27,000 * 1.08 = $29,160

Year 3: $29,160 * 1.08 = $31,492.80

Year 4: $31,492.80 *1.08 = $34,012.22

Year 5: $34,012.22 * 1.08 = $36,733.20

Year 6: $36,733.20 * 1.08 = $39,671.86

Year 7: $39,671.86 * 1.08 = $42,845.61

Year 8: $42,845.61 * 1.08 = $46,273.26

Year 9: $46,273.26 * 1.08 = $49,975.12

Year 10: $49,975.12 * 1.08 = $53,973.13

An easier way to calculate the final amount is to use exponentials. $25,000 * (1.08)^10 = $53,973.13.