Payout annuities

Question

How much would you need to deposit in account each month in order to have $50,000 in the account in nine years assume the account earns 3% annual interest compounded monthly

Answer 1

Hi Richard!

According to the question, the amount accumulated in the account is:

A = $50,000

Rate of interest is R = 3% = 0.03 annually.

If interest is compounded monthly the periodic interest rate is:

I = R / 12 = 0.03 / 12 = 0.0025

The period of payments is:

N = 9 years = 9 × 12 = 108 months

As payments are deposited at the end of the period so given annuity is an ordinary annuity. The amount deposited in an ordinary annuity to have an accumulated value is given by:

C = A × i / (1+i)^n - 1

Substitute the values and solve for periodic deposits. The amount need to be deposited at the end of each month is:

C = 50,000 × 0.0025 / (1 + 0.0025)^108 - 1

C = $403.85

The amount need to be deposited at the end of each month is:

$403.85