Matthew saves $10,000 at the end of each month for the next 25 years, after whic
ID: 2727111 • Letter: M
Question
Matthew saves $10,000 at the end of each month for the next 25 years, after which he retires. During the first seven years of retirement, he withdraws $60000 at the start of each month, after which he dies. His son, Sean, inherits the remainder of Matthew's savings. It is further stipulated in Matthew's will that Sean will be paid the money in equal payments, at the start of every month, for the next 18 years. Given a fixed interest rate of 9% p.a., calculate the monthly payment that Sean will receive.
A) $129,781 B) $184,034 C)$204,444 D) $188,656 E) $173,258 F $231,512 no need for process, asap ,ty)
Explanation / Answer
Compound Value of an annuity=FV=A*[ (1+r)^n - 1)]/r Where, A=Amount deposited every month=10000, r=interest=0.09/12=0.0075, n=period=25*12=300 FV at end of 25th year=10000*(1.0075^300-1)/0.0075 11211219.37 PV of 60000 received in the first 7 years Present Value of an Annuity due=PV= A*[(1+r)^n - 1]*(1+r)/[(1+r)^n)*r] PV=60000*(1.0075^84-1)*(1.0075)/((1.0075^84)*(0.0075)) 3757207.158 Balance receivable at the retirement of Mathew (PV Value) 7454012.215 Amount receivable after 7years=7454012.215*(1.09^7) 13626225.94 This amount should be the PV of 216 months of payment that Sean will get . Let that amount me A PV=A*(1.0075^216-1)*(1.0075)/((1.0075^216)*(0.0075)) 13626225.94 or A=13626225/107.58 126661.322 So the answer will be (A) which is the closest amount.