Math problem, help pls!

Question

Suppose you want to have $300,000 for retirement in 35 years. Your account earns 4% interest. How much would you need to deposit in the account each month?

Answer 1

There is probably a formula for this in the class you are taking. Or you can derive the solution because it is a geometric series:

1st Payment will be worth P(1+.04/12)^35*12 after 35 years

2nd Payment: P(1+.04/12)^35*12-1

nth Payment: P(1+.04/12)^35*12-n

The sum of the payment value (=300000) = P(sum from 1 to 420 of (1.+.04/12)^420-n)

The part in parentheses has the sum of (1-r⁴²⁰)/(1-r) where r is (1+.04/12)

I get P = 300000/913.7309 = 328.32 (note that 137K or so was paid in)

Please consider a tutor. Take care.