Beginning three months from now, you want to be able to withdraw $1,900 each quarter from your bank account to cover college expenses over the next five years. if the account pays 0.41 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next five years?

Question

Mathematics

Ruffe

7 August, 10:08

Beginning three months from now, you want to be able to withdraw $1,900 each quarter from your bank account to cover college expenses over the next five years. if the account pays 0.41 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next five years?

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Answers (1)

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Spot · Answer 1

Compounding period = quarter (3 months)

Account interest per period (quarter), i = 0.41%

Number of periods over 5 years, n = 5*4 = 20

Quarterly withdrawal Amount, A = 1900

Initial deposit (today) = P

We match/equate the future value of the deposit and the withdrawals to calculate the deposit amount P needed.

Future value of deposit

F1=P (1+i) ^n

=P (1.0041) ^20

Future value of withdrawals

F2=A ((1+i) ^n-1) / i

=1900 ((1.0041^20-1) / 0.0041

Equate F1=F2

P (1.0041) ^20=1900 (1.0041^20-1) / 0.0041

=>

P=1900 (1.0041^20-1) / 0.0041 / (1.0041^20)

=$36412.15 (to the nearest cent)

Answer: A deposit of $36412.15 is needed today to cover the future withdrawals.