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

Answer:

$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.