The Power of Compound Interest

Suppose that you give your child $1 on her 5th birthday. To encourage her to save her money, you offer to pay interest of 10% per month on any money that she has saved at the end of each month.

How large will that one dollar have grown by her 18th birthday? (Assume she turned 18 on the last day of the month and collected her last interest payment on that day, so that she received interest for 13 years * 12 months = 156 times. Hint: In the formula at the top of the assignment, n=156 months, and r=10% per month.)

(Round to the nearest dollar.)

Takeaway:

Be careful what you promise your kids.

Another takeaway:

As your money grows, the return on your investment (i.e., interest in this example), gets larger and larger. If you keep reinvesting the interest so that you are earning interest on the interest, your money grows faster and faster over time.

Similarly, if you are in debt and stop making payments, the unpaid interest begins to accumulate and is added to your loan balance. In future periods, they charge you interest on the original balance and on the unpaid interest. Over time, your loan balance will start to grow faster and faster as the interest charges that are getting added to your outstanding loan balance get larger and larger (because you are paying interest on a larger and larger balance of unpaid interest, in addition to paying interest on the original loan balance).

Note: Suppose that you give your child $1 of allowance per week (starting at age 5 and ending at age 18), with the same deal described above (you will pay 10% interest per month on her savings). If she saves all of her allowance, she would end up with about $114.6 million on her 18th birthday. (That is the future value of an annuity of $4/month received each period and reinvested at 10% per period for 156 periods.) We actually gave our daughter this deal when she was 5 but had to change the terms of the agreement a couple years later when we realized that her bank balance was growing way too fast because she never spent her money.