Question

How do you find the present value that will grow to $20,000 if interest is 7% compounded quarterly for 15 quarters?

Answer 1

$15 417.49

Explanation:

The formula for compound interest is `A=P(1+i)^n`.
`A` represents the final amount that that account has grown to,
`P` represents the starting amount of money (usually called the principal or present value),
`i` represents the interest rate per compound, and
`n` represents the number of compounds.

In this question, `A=20 000`, `P` is the unknown value, `i`
is `0.07/4` since there are 4 compounding periods per year when the interest is compounded quarterly, and `n` is 15.

`A=P(1+i)^n`
`20 000=P(1+0.07/4)^15`
`20 000=P(1+0.0175)^15`
`20000=P(1.0175)^15`
`20000=P(1.297227864)`

Dividing both sides by (1.297227864) gives us
`20000/(1.297227864) = P`

The answer is `P=15417.49`

Thus, $15 417.49 will grow to $20 000 if interests is 7% compounded quarterly for 15 quarters.