Question

A company wants to have $60,000 at the beginning of each 6-month period for the next 4 1 2 years. If an annuity is set up for this purpose, how much must be invested now if the annuity earns 6.04%, compounded semiannually?

Answer 1

Answer:

$466,680.

Explanation:

The annual interest rate is 6.04%. It is compounded anually.

The number of periods is 2*4.5=9 semesters.

The interest rate per period is i=0.0604/2=0.0302.

The annuity factor is:

$An=\frac{1-(1+i)^{-n}}{i} =\frac{1-(1.0302)^{-9}}{0.0302} =\frac{1-0.7651}{0.0302} \\\\An=\frac{0.2349}{0.0302}= 7.778$

Then, the capital that is needed to be invested now to get $60,000 for 4.5 years is:

$C=P*An=60,000*7.778=466,680$