A money manager has $1,000,000 to invest for one year. She has identified two alternative one-year certificates of deposit (CD) shown below: Compounding frequency Annual interest rate CD1 Quarterly 8.00% CD2 Continuously 7.95% Which CD has the highest effective annual rate (EAR) and how much interest will it earn? Highest EAR Interest earned A.CD1 $81,902 B.CD1 $82,432 C.CD2 $82,746 D.CD2 $83,287
C) Obviously we know that the continuous has the higher yield. You can solve for the continuous compounding using the e^x function… or you can simply enter it in the the TVM For N, select so randomly high number… like 1000. And then for the rate, do 7.95/1000. You’ll get a very close approximate of continuous that way.
CD1: (1+.08/4)^4 = 1.0824 = 8.24% Interest earned from a mil: 82,432.16 CD2 e^.0795 = 1.0827 = 8.27% (On the TI, just type .0795 [2nd] [LN]) Interest earned from a mil: 82,745.56 Answer is C
When dealing with continuous compounding, remember: 1) When entering e^x, make sure you DON’T add 1 2) When you get your continuously compounded interest rate, you will MINUS one. 3) When you want to go from a continuously compounded rate back you an annual rate you ADD one, and take the log (push the [LN] key) Hope that helps