Question

I invested $15,000 at the end of each year for 20 years, earning an average of 8% per year, then $20,000 at the end of each year for the next 20 years earning an average of 4 percent per year. I then contacted Annuity Corp. which offers annuities to retirees. If I receive an annual interest rate of 2.5%, how much could I receive at the end of each of the following 20 years if I invested my retirement savings?

Answer 1

The time horizon for the investment is 40 years, first 20 years

Amount invested (P) = $15,000

i = 8%

n = 20 years

Using the formula for calculating future value :

Putting values in the formula :

FV of annuity = 15,000 * 45.76 = $686,429.46. This is the value after first 20 years.

Value of this investment further after 20 years would be $686.429.46 * (1+4%)^20 = $1,504,051.49 (A)

Value of second annuity would be :

i = 4%

n = 20 years

P = $20,000

FV = 20,000 * 29.78 = $595,561.57 (B)

Total value of savings after 40 years will be (A+B) = $2,099,613.06

The person wants to withdraw this amount for 20 years in annuity.

PV of that annuity will be equal to the initial investment amount of $2,099,613.06

PV formula :

PV = $2,099,613.06

i = 2.5%

n = 20 years

putting values in formula :

$2,099,613.06 = C * 15.59

C = $134,684.15 per year.