Question

5-24 FUTURE VALUE OF AN ANNUITY Find the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually b. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur

Answer 1

the effective interest rate is different

Step-by-step explanation:

the nominal rate for both annuities is the same, 12% annual, but the compounding periods differ. One annuity is compounded semiannually while the other is compounded quarterly.

effective interest rate semiannual payments = (1 + 12%/2)² - 1 = 12.36%

effective interest rate quarter payments = (1 + 12%/4)⁴ - 1 = 12.55%