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

1 Answer
Mar 20, 2018

$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.