How much would need to be deposited into an account earning 4.7%, compounded quarterly, so that the balance will be $1,000,000.00 in 20 years?

1 Answer
Jun 16, 2018

You would need to deposit $392,774.20

Explanation:

Compound interest formula: #A=P(1+r/n)^(nt)#

A = Final amount
P = Initial deposit
r = Interest rate
n = Compound period (times per year)
t = Number of years

1 - Substitute known values

#1000000=P(1+0.047/4)^(4(20))#

2 - Simplify as needed

#1000000=P(4/4 + 0.047/4)^80#
#1000000=P(4.047/4)^80#

3 - Rearrange to find P

#P = (1000000)/(4.047/4)^80 = 392774.20#

4 - Check your answer

#A = $392774.20(1+0.047/4)^(4(20)) ~= $1000000#

edit: fixed bullet points