Question

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.

Answer 1

Answer:

The amount of each withdrawal is $21368.46

and amount of each withdrawal if the money must last 5 years is  $17584.57

Step-by-step explanation:

given data

principal = $150000

rate = 6% per year = (6/2 )× 100  = 0.03 compound semiannually

time period = 4 year = 4× 2 = 8 half yearly

time period =  5 year = 5 × 2 = 10 half yearly

to find out

The amount of each withdrawal and he amount of each withdrawal if the money must last 5 years

solution

first we solve to find payment to each withdraw in 4 year i.e. formula

amount = principal (rate ) / 1- $(1+rate)^{-time}$    ...........1

put all value rate principal time 8 half yearly in equation 1

amount = principal (rate ) / 1- $(1+rate)^{-time}$  

amount = 150000 (rate ) / 1- $(1+0.03)^{-8}$  

amount = 150000 (0.03 ) / 1- $(1+0.03)^{-8}$  

amount = 21368.458324

The amount of each withdrawal is $21368.46

now we solve to find payment to each withdraw in 5 year i.e. formula

amount = principal (rate ) / 1- $(1+rate)^{-time}$    ...........2

put all valye rate principal time in equation 2

amount = principal (rate ) / 1- $(1+rate)^{-time}$  

amount = 150000 (rate ) / 1- $(1+0.03)^{-10}$  

amount = 150000 (0.03 ) / 1- $(1+0.03)^{-10}$  

amount = 17584.575991

amount of each withdrawal if the money must last 5 years is  $17584.57