Find the future values of the following ordinary annuities. a. FV of $400 each 6
ID: 2703905 • Letter: F
Question
Find the future values of the following ordinary annuities.
a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded
semiannually
b. FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly
c. The annuities described in parts a and b have the same total amount of money paid
into them during the 5-year period, and both earn interest at the same nominal rate,
yet the annuity in part b earns $101.75 more than the one in part a over the 5 years.
Why does this occur?
Find the future values of the following ordinary annuities. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly The annuities described in parts a and b have the same total amount of money paid into them during the 5-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over the 5 years. Why does this occur?Explanation / Answer
a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded
semiannually
FV = 400 FVIFA(6%,10) = $5272.32
b. FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly
FV = 200 FVIFA(3%,20) = $5374.07
c. The annuities described in parts a and b have the same total amount of money paid
into them during the 5-year period, and both earn interest at the same nominal rate,
yet the annuity in part b earns $101.75 more than the one in part a over the 5 years.
Why does this occur?
It is due to change of compounding i.e in part b the interest amount is being compounded quarterly and in part a the interest amount is being compounded semi annually , so the difference arises due to interest on interest is being calculated faster , if we have to compare than it must be compare with effective rate not with nominal rate, The effective rate is higher in part B than Part A
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