Question

You want to borrow $600,000 to buy an apartment, and you can only afford $4,000 a month to repay the loan. Suppose the bank charges you a fixed interest rate of 4% with monthly compounding. How long will it take you to pay off the loan

Answer 1

Answer :

Loan for Apartment = $ 6,00,000

Monthly repayment of Loan Installment = Principal Payment + Interest = $ 4,000

Bank Interest rate = 4% per year fixed with monthly compounding

Monthly Interest rate = 4% /12 = 0.33% = 0.0033

Number of Months be n

= [ $600000 + ( $600000 x ( ( 1+0.0033)n-1 )) ] / n = $4000

4000n = [ $600000 + ( $600000 x ( ( 1+0.0033)n-1 )) ]

Taking Log of Both Sides

Log ( 4000) + Log n = Log [ $600000 + ( $600000 x ( ( 1+0.0033)n-1 )) ]

3.6021 + Log n = 5. 7782 + (5.7782 + ( n x 0.0140 -0 )

Log 3.6021 n = 11.5564 + 0.0140 n

Taking Antilog of Both Sides

Antilog ( 3.6021 Log n ) = Antilog ( 11.5564 ) + n x Antilog ( 0.0140 )

4000 n = 1200000+ ( -3 + 0.1033 ) n

n = 300 months

It means 25 years ( 300 months / 12 ) is the period of Loan

n = 25 years