Q:

The trustees of a college have accepted a gift of $150000, but are required to deposit it in an account paying 6% per year, compounded semiannually. They may make equal withdrawals at the end of each six-month period, but the money must last 4 years. a. The amount of each withdrawal is $ (Round your answer to the nearest cont.) b. If the money must last 5 years, the amount of each withdrawal is (Round your answer to the nearest cont.) a. Find the amount of each withdrawal. b. Find the amount of each withdrawal if the money must last 5 years.

Accepted Solution

A:
Answer:The amount of each withdrawal is $21368.46and amount of each withdrawal if the money must last 5 years is  $17584.57Step-by-step explanation:given dataprincipal = $150000rate = 6% per year = (6/2 )× 100  = 0.03 compound semiannuallytime period = 4 year = 4× 2 = 8 half yearlytime period =  5 year = 5 × 2 = 10 half yearlyto find out The amount of each withdrawal and he amount of each withdrawal if the money must last 5 yearssolution first we solve to find payment to each withdraw in 4 year i.e. formulaamount = principal (rate ) / 1- [tex](1+rate)^{-time}[/tex]    ...........1put all value rate principal time 8 half yearly in equation 1amount = principal (rate ) / 1- [tex](1+rate)^{-time}[/tex]  amount = 150000 (rate ) / 1- [tex](1+0.03)^{-8}[/tex]  amount = 150000 (0.03 ) / 1- [tex](1+0.03)^{-8}[/tex]  amount = 21368.458324The amount of each withdrawal is $21368.46now we solve to find payment to each withdraw in 5 year i.e. formulaamount = principal (rate ) / 1- [tex](1+rate)^{-time}[/tex]    ...........2put all valye rate principal time in equation 2amount = principal (rate ) / 1- [tex](1+rate)^{-time}[/tex]  amount = 150000 (rate ) / 1- [tex](1+0.03)^{-10}[/tex]  amount = 150000 (0.03 ) / 1- [tex](1+0.03)^{-10}[/tex]  amount = 17584.575991amount of each withdrawal if the money must last 5 years is  $17584.57