Question

Assume that 25 years ago your dad invested $380,000, plus $31,000 in years 2 through 5, and $46,000 per year from year 6 on. Determine the annual retirement amount that he can withdraw forever starting next year (year 26), if the $46,000 annuity stopped at year 25. The interest rate being 14% per year.

The annual retirement amount is determined to be $_.

Answer 1

Maturity value of $380,000 for 25 years , MV1 = P (1+r/n) ^ (n x t)

P = Principal amount invested

r = Annual Rate of Interest (in decimals)

n = number of compounding in a year = 1

t = number of years

MV1 = P (1+r/n) ^ (n x t) = 380000 x ( 1 + 0.14 / 1) ^ (1 x 25)

= $10055528.01

Maturity value of $31,000 for 4 years (year 2 through 5) , MV2 = P x N x [ 1 + ((N+1) x r / 24) ]

N = number of terms in months

P = Installment Amount per month

r = Annual Rate of Interest (in decimals)

Hence, MV2 = (31000 / 12) x (48) x [ 1 + ((48+1) x 0.14 / 24) ]

= $159,443.33

Similarly, Maturity value of $46,000 for 20 years (year 6 through 25) , MV3 = P x N x [ 1 + ((N+1) x r / 24) ]

N = number of terms in months

P = Installment Amount per month

r = Annual Rate of Interest (in decimals)

Hence, MV3 = (46000 / 12) x (240) x [ 1 + ((240+1) x 0.14 / 24) ]

= $2213366.667

Total Maturity Value = MV1 + MV2 + MV3

= $10055528.01 + $159,443.33 + $2213366.667

= $12428338.01

Hence, Annual Retirement Amount at 14% interest rate = Total Maturity Value * Annual Interest Rate

= $12428338.01 x 0.14

= $1739967.321