read the eBook: Future Value of an Ordinary Annuity Problem 4-18 Future Value of
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read the eBook: Future Value of an Ordinary Annuity
Problem 4-18
Future Value of an Annuity for Various Compounding Periods
Find the future values of the following ordinary annuities:
FV of $200 paid each 6 months for 8 years at a nominal rate of 12%, compounded semiannually. Round your answer to the nearest cent.
$
FV of $100 paid each 3 months for 8 years at a nominal rate of 12%, compounded quarterly. Round your answer to the nearest cent.
$
The annuities described in parts a and b have the same amount of money paid into them during the 8-year period and both earn interest at the same nominal rate, yet the annuity in part b earns more than the one in part a over the 8 years. Why does this occur?
-Select-The nominal deposits into the annuity in part (b) are greater than the nominal deposits into the annuity in part (a).The annuity in part (a) is compounded less frequently; therefore, more interest is earned on interest.The annuity in part (a) is compounded more frequently; therefore, more interest is earned on interest.The annuity in part (b) is compounded less frequently; therefore, more interest is earned on interest.The annuity in part (b) is compounded more frequently; therefore, more interest is earned on interest.Item 3
Explanation / Answer
a.PMT = $200
Nper = 8 x 2 = 16 periods
Rate = 12%/2 =6%
FV ordinart annuity (calculated in excel) = $5134.51
b.
PMT = $100
Nper = 8 x 4 = 32 periods
Rate = 12%/4 =3%
FV ordinart annuity (calculated in excel) = $5250.28
The annuity in part (b) is compounded more frequently; therefore, more interest is earned on interest.
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