Question

Suppose you want to have $300,000 for retirement in 30 years. Your account earns 4% interest.

a) How much would you need to deposit in the account each month?

b) How much interest will you earn?

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Future value	300000
Time	30
Interest	4%
300000=	Annual Deposit * ((((1 + 4%) ^ 30) - 1) / 4%)
300000=	Annual Deposit * 56.08493
Annual deposit	=300000/56.08493
Annual deposit	5,349.03
Total contribution=	5349.03*30
Total contribution=	160,470.90
Total Interest=	300000-160470.9
Total Interest=	139,529.10