Question

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?

Answer 1

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