Question

In: Finance

Future Value of an Annuity for Various Compounding Periods Find the future values of the following...

Future Value of an Annuity for Various Compounding Periods

Find the future values of the following ordinary annuities.

  1. FV of $600 each 6 months for 4 years at a nominal rate of 12%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

    $  

  2. FV of $300 each 3 months for 4 years at a nominal rate of 12%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent.

    $  

  3. The annuities described in parts a and b have the same amount of money paid into them during the 4-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 4 years. Why does this occur?

Solutions

Expert Solution

a

FV of annuity = P * [ (1+r)^n -1 ]/ r
Periodic payment P= $                   600.00
rate of interest per period r=
Rate of interest per year 12.0000%
Payment frequency Once in 6 months
Number of payments in a year                            2.00
rate of interest per period 0.12*6/12 6.0000%
Number of periods
Number of years                                  4
Number of payments in a year                                  2
Total number of periods n=                                  8
FV of annuity = 600* [ (1+0.06)^8 -1]/0.06
FV of annuity =                    5,938.48

Future value is $5,938.48

b

FV of annuity = P * [ (1+r)^n -1 ]/ r
Periodic payment P= $                   300.00
rate of interest per period r=
Rate of interest per year 12.0000%
Payment frequency Once in 3 months
Number of payments in a year                            4.00
rate of interest per period 0.12*3/12 3.0000%
Number of periods
Number of years                                  4
Number of payments in a year                                  4
Total number of periods n=                               16
FV of annuity = 300* [ (1+0.03)^16 -1]/0.03
FV of annuity =                    6,047.06

Future value is $6,047.06

c

Difference is due to difference in compounding of interest. More number of compounding intervals in quarterly payment resulted in highe interest.

please rate.


Related Solutions

Future Value of an Annuity for Various Compounding Periods Find the future values of the following...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of $400 each 6 months for 10 years at a nominal rate of 16%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. FV of $200 each 3 months for 10 years at a nominal rate of 16%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $
Future Value of an Annuity for Various Compounding Periods Find the future values of the following...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of $600 each 6 months for 9 years at a nominal rate of 12%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. $    FV of $300 each 3 months for 9 years at a nominal rate of 12%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $    The annuities...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of $800 each 6 months for 9 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. $ FV of $400 each 3 months for 9 years at a nominal rate of 8%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $ The annuities...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of $200 each 6 months for 5 years at a nominal rate of 8%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. $   FV of $100 each 3 months for 5 years at a nominal rate of 8%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $   The annuities...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following...
Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities. FV of $800 each 6 months for 9 years at a nominal rate of 12%, compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent. $   FV of $400 each 3 months for 9 years at a nominal rate of 12%, compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $   The annuities...
Problem 4-18 Future Value of an Annuity for Various Compounding Periods Find the future values of...
Problem 4-18 Future Value of an Annuity for Various Compounding Periods Find the future values of the following ordinary annuities: FV of $600 paid each 6 months for 6 years at a nominal rate of 8%, compounded semiannually. Round your answer to the nearest cent. $     FV of $300 paid each 3 months for 6 years at a nominal rate of 8%, compounded quarterly. Round your answer to the nearest cent. $    
Present Value for Various Compounding Periods Find the present value of $575 due in the future...
Present Value for Various Compounding Periods Find the present value of $575 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent. 9% nominal rate, semiannual compounding, discounted back 5 years. $   9% nominal rate, quarterly compounding, discounted back 5 years. $   9% nominal rate, monthly compounding, discounted back 1 year. $  
5-14 Future Value of An Annuity Find the future values of these ordinary annuities. Compounding occurs...
5-14 Future Value of An Annuity Find the future values of these ordinary annuities. Compounding occurs one a year. a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Rework parts a, b, c assuming they are annuities due.
Future value for various compounding periods Find the amount to which $200 will grow under each...
Future value for various compounding periods Find the amount to which $200 will grow under each of these conditions: 16% compounded annually for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $   16% compounded semiannually for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $   16% compounded quarterly for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $   16% compounded monthly for...
Problem 4-16 Future Value for Various Compounding Periods Find the amount to which $550 will grow...
Problem 4-16 Future Value for Various Compounding Periods Find the amount to which $550 will grow under each of the following conditions. Do not round intermediate calculations. Round your answer to the nearest cent. 9% compounded annually for 5 years $    9% compounded semiannually for 5 years $    9% compounded quarterly for 5 years $    9% compounded monthly for 5 years $  
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT