Question

Problem 4 and 5-3 Future Value and Number of Annuity Payments

Your client has been given a trust fund valued at $1.12 million. He cannot access the money until he turns 65 years old, which is in 25 years. At the time, he can withdraw $24,000 per month.

If the trust fund is invested at a 5.0 percent rate, how many months will it last your client once he starts to withdraw the money? (Assume annual compounding. Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Future value = present value*(1+ rate)^time

Future value = 1120000*(1+0.05)^25

Future value = 3792717.53

Assuming ordinary annuity (please let me know if anwer is not correct , it may be annuity due, not clear in the question)

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

3792717.53380731= 24000*((1-(1+ 5/1200)^(-n*12))/(5/1200))

n(in years) = 21.53

Months = 21.53*12=258.36 months