EXAMPLE 11 Certificates of Deposit

A certificate of deposit (CD) pays a fixed rate of interest for a term specified in advance, which may range from 1 month to 10 years. The best local rate in June 2015 was for a 60-month CD at 0.747%, compounded daily. How much would need to have been set aside in such a CD to have $12,000 in 60 months?

We find the present value of receiving $12,000 60 months from now, with , and , so that . (Fine point: We use despite the fact that one or two leap days will occur during the 5 years. For a leap year, the bank may apply a daily rate of either 1/366 or 1/365 of the interest rate for the year. We neglect those complications, which would make little difference.) The present value formula gives