FUTURE VALUE OF AN ANNUITY Find the future values of the following ordinary annu

Question

FUTURE VALUE OF AN ANNUITY

Find the future values of the following ordinary annuities:

FV of $500 paid each 6 months for 5 years at a nominal rate of 9% compounded semiannually. Round your answer to the nearest cent.
$  

FV of $250 paid each 3 months for 5 years at a nominal rate of 9% compounded quarterly. Round your answer to the nearest cent.
$  

___________________________________________

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?

A.The nominal deposits into the annuity in part (b) are greater than the nominal deposits into the annuity in part (a).

B.The annuity in part (a) is compounded less frequently; therefore, more interest is earned on previously-earned interest.

C.The annuity in part (a) is compounded more frequently; therefore, more interest is earned on previously-earned interest.

D.The annuity in part (b) is compounded less frequently; therefore, more interest is earned on previously-earned interest.

E.The annuity in part (b) is compounded more frequently; therefore, more interest is earned on previously-earned interest.

Explanation / Answer

a) Future value of ordinary annuity = payment [ (1+interest)number of payment - 1 ] / interest

=500 [ (1+0.045)2*5- 1 ] / 0.045

=500 [ (1.045)10- 1 ] / 0.045

=500 [ 1.55297 - 1 ] / 0.045

=500 *12.28822

= 6144.11

b) Future value of ordinary annuity = payment [ (1+interest)number of payment - 1 ] / interest

= 250 [ (1+0.0225)4*5- 1 ] / 0.0225

= 250 [ (1.0225)20- 1 ] / 0.0225

= 250 [ 1.56051 - 1 ] / 0.0225

= 250 *24.91156

= 6227.89

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