Question

An ordinary annuity was purchased 5 years ago. The annuity pays 8%compounded quarterly. The quarterly payments have been $500. What is the amount of interest earned on the annuity to date?

Answer 1

"$8,175.72" is the right solution.

Step-by-step explanation:

The given values are:

Periodic payments,

C = $500

Interest rate,

r = 8%

i.e.,

=
`(8)/(4)` =
`2`%

Number of periods,

n = 5 years,

i.e.,

=
`5* 4` =
`20`

As we know,

The present value of annuities 5 years ago will be:

⇒
`Present \ Value =C* ([1-(1+r)^(-n)])/(5)`

On substituting the given values, we get

⇒
`=500* ([1-(1+0.02)^(-20)])/(0.02)`

⇒
`=500* (1-0.6729713331)/(0.02)`

⇒
`=500* 16.35143335`

⇒
`=8,175.72` ($)