Question

Ramogi and Amelia have a new grandson . How much money should they invest now so that he will have \$40,000 for his college education in 18 years ? The money is invested at 7.6\% compounded quarterly .

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The initial amount (principal).

Given:

Amount(final) = $40000

time = 18

rate(r)=7.6% =0.076

n=4

Step 1

Recall th compound interest formula.

`A=P(1+(r)/(n))^(nt)`

Step 2

Substitute the values into the formula.

`40000=P(1+(0.076)/(4))^((4)(18))`
`40000=P(1+0.019)^(72)`

Step 3

Simplify and solve for p.

`40000=P(1.019)^(72)`
`40000=p(3.87740573623)`

Divide both-side of the equation by 3.87740573623

`P\approx10316.18`

ANSWER

The amount to be invested now is 10316.18