The trustees of a college have accepted a gift of $475000, but are required to deposit it m an account payıng 10% per year, compounded semiannually. They may make equal withdrawals at the end of each sx-month period, but the money must last 7 years. Find the amount of each withdrawal Find the amount of each withdrawal if the money must last 9 years.

Aleseelomnl

Aleseelomnl

Answered question

2022-08-08

The trustees of a college have accepted a gift of $475000, but are required to deposit it m an account payıng 10% per year, compounded semiannually. They may make equal withdrawals at the end of each sx-month period, but the money must last 7 years. Find the amount of each withdrawal Find the amount of each withdrawal if the money must last 9 years.

Answer & Explanation

Kelton Glover

Kelton Glover

Beginner2022-08-09Added 17 answers

Present Value ordinary annuity, PV = $475,000
Payment each period =A
As interest 1s compoun ded semi annually (twice per year),
Interest rate per period, i = 10 2
= 0.10 2
=0.05
Find the amount of each withdrawal if the money must last 7 years.
Number of compounding periods,
n=7 years × 2 compounding periods per year
= 14.
Recollect Present Value of Ordinary annuity
(annuity with payments at the end of each period).
P V = A [ 1 ( 1 + i ) n i ]
475000 = A [ 1 ( 1 + 0.05 ) 14 0.05 ]
A = 475000 × 0.05 1 ( 1.05 ) 14
47986.38549
Therefore, the required amount is $47986.39
Find the amount of each withdrawal if the money must last 9 years.
Number of compounding periods,
=9 years × 2 compounding periods per year
= 18.
Present Value of Ordinary annuity,
P V = A [ 1 ( 1 + i ) n i ]
475000 = A [ 1 ( 1 + 0.05 ) 18 0.05 ]
A = 475000 × 0.05 1 ( 1.05 ) 18
40634.4556
Therefore, the required amount is $40634.46

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