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

Answer:

"$8,175.72" is the right solution.

Explanation:

The given values are:

Periodic payments,

C = $500

Interest rate,

r = 8%

i.e.,

 = $\frac{8}{4}$ = $2$%

Number of periods,

n = 5 years,

i.e.,

  = $5\times 4$ = $20$

As we know,

The present value of annuities 5 years ago will be:

⇒  $Present \ Value =C\times \frac{[1-(1+r)^{-n}]}{5}$

On substituting the given values, we get

⇒                           $=500\times \frac{[1-(1+0.02)^{-20}]}{0.02}$

⇒                           $=500\times \frac{1-0.6729713331}{0.02}$

⇒                           $=500\times 16.35143335$

⇒                           $=8,175.72$ ($)