Question

1-if we do not want to make monthly car payments over $450, up to what amount can I borrow today if r = 3% APR compounded monthly, and the loan requires 60 monthly payments?

2-Our clients saved $2,500,000 for retirement. They wish to withdraw $20,000 from the fund each month for expenses. How long will their retirement savings last if the fund is earning 9% APR compounded monthly?

please answer both questions for full rate

Answer 1

Ques-1)

Maximum Monthly Car Payments = $450

Calculating the Loan amount:-

Where, P = Loan amount

r = Periodic Interest rate = 3%/12 = 0.25%

n= no of periods = 60

Monthly Payments = $450

P = $25043.56

So, amount can be borrowed today is $25,043.56

Ques-2)

Present Value of Retirement = $2,500,000

Each monthly withdrawal = $20,000

Calculating the no of period it would take to Retirement to last:-

Where, C= Periodic Withdrawal = $20,000

r = Periodic Interest rate = 9%/12 = 0.75%

n= no of periods

Present Value = $2,500,000

0.9375 = 1 - (1.0075)^(-n)

(1.0075)^(-n) = 1 - 0.9375

(1.0075)^(-n) = 0.0625

Taking log on both sides,

Log[(1.0075)^(-n)] = Log(0.0625)

-n*Log(1.0075) = Log(0.0625)

-n(0.00324505) = -1.20411998

n = 371.06

So, it would take 371 months to last the Retirement fund.

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