Question

Suppose you have 25 years until you retire, and that you desire a retirement nest-egg of $2,500,000 on the day you retire. Suppose also that you’ve saved $100,000 toward your retirement so far, and that your investment account earns a nominal rate of 7.5% per year, compounded monthly. In addition, suppose you expect a windfall inheritance of $200,000 five years from now that you will invest in this account.

a) What is the effective interest rate, or annual percentage yield, of your investment account?

b) How much money should you deposit into that account every year in order to reach your goal?

Answer 1

a]

effective interest rate = (1 + r/n )ⁿ – 1

where r = nominal rate

n = number of compounding periods per year (12 in this case because of monthly compounding)

effective interest rate = (1 + (7.5% / 12))¹² - 1 = 0.0776, or 7.76%

b]

Value of $200,000 at end of 25 years from now =  $200,000 * (1 + effective interest rate)^25-5

Value of $200,000 at end of 25 years from now = $200,000 * (1 + 7.76%)²⁰ = $891,624

The annual deposit is calculated using PMT function in Excel :

rate = 7.76% (effective interest rate)

nper = 25 (25 deposits in total)

pv = -100,000 (amount already saved. This is entered as a negative number because it is like a payment into the fund now)

fv =  2,500,000 - 891,624 (inheritance amount will accumulate to $891,624 at the end of 25 years. This is deducted from the final retirement fund required)

PMT is calculated to be 13,607

annual deposit required is $13,607