Suppose you want to have $500,000 for retirement in 30 years. Your account earns 5% interest. How much would you need to deposit in the account each month?

Answer 1

present value of an annuity:

PV = P * ((1 - (1 + r)^(-n)) / r)

Where: PV = present value or desired future value ($500,000) P = monthly deposit r = interest rate per month (5%/12 = 0.0041667) n = number of months (30 years x 12 months/year = 360 months)

Plugging in the values, we get:

500,000 = P * ((1 - (1 + 0.0041667)^(-360)) / 0.0041667)

Solving for P, we get:

P = 500,000 / ((1 - (1 + 0.0041667)^(-360)) / 0.0041667)

P = $702.58 per month (rounded to the nearest cent)

Therefore, you would need to deposit $702.58 into the account each month to reach $500,000 for retirement in 30 years, assuming an interest rate of 5%.