Question

If upon graduating on your 25 th birthday, you were able to save $3000 per year for eight full
years (EOY 25-32) until you were married, how much is the savings worth until your retirement
at the end of your 66 th year, assuming the annual interest rate was 10% throughout, and you did
not withdraw any of the principal or interest until then? Draw a cash flow diagram, including
the value of the annuity at both years 32 and 66.

Answer 1

Age	25	26	27	28	29	30	31	32	33	34			66
Amount	3000	3000	3000	3000	3000	3000	3000	3000
Future value of an annuity = C[((1+r)^t-1)/r]
where C is the annuity payment that is 3000
r is the interest rate that is .10
t is the year
Future value of annuity in 8 years = 3000*[(((1.10)^8)-1)/.10]
Future value of annuity in 8 years = 34307.66
The value of the annuity at age 32 = $34307.66
Future Value = Present Value*((1+r)^t)
where r is the interest rate that is .10 and t is the time period that is (66 - 32) 34 years
Present value = 34307.66
Future Value = 34307.66*((1.10)^34)
The value of the annuity at age 66 = $876480.77