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start-up entrepreneur wants to determine how much he can borrow in the form of a fixed-rate...

start-up entrepreneur wants to determine how much he can borrow in the form of a fixed-rate 20-year loan from bank. The loan for 20 years carries a fixed interest rate of 9.00%. He estimates that he can pay a maximum of $25,000 annual repayment (interest plus principal).

How large a loan can he afford, assuming he makes steady repayments of $25,000 per year for 20 years? How much total interest will be paid over the 20-year life of the mortgage? How much interest will be paid during the first year of the mortgage? How much principal will be repaid in the first year? How much of the final $25,000 payment at the end of 20 years will be interest and how much will be principal?

Solutions

Expert Solution

We will have to calculate the maximum loan amount by using the PV function
Amount of loan = Annual payment*(1-(1+r)^-n)/r
Amount of loan = 25000*(1-(1+0.09)^-20)/0.09
Amount of loan = 25000*(1-(1.09)^-20)/0.09
Amount of loan = 25000*9.128546
Amount of loan $228,213.64
The loan that can be taken is $228,213.64
Total payment on loan 25000*20 $500,000.00
Loan amount $228,213.64
Total interest paid on loan $271,786.36
The total interest paid on loan is the difference between the total payment made over 20 years and the loan amount
Interest payment in first year = Loan amount*Interest rate
Interest payment in first year = 228213.64*9%
Interest payment in first year $20,539.23
Principal repaid in first year = Annual payment - Interest payable in first year
Principal repaid in first year = 25000 - 20539.23
Principal repaid in first year $4,460.77
We will have to calculate the balance of loan at end of 19 years so as to calculate interest and principal repayment
Loan balance at end of 19 years 25000*(1-(1.09^-1)/0.09
Loan balance at end of 19 years 25000*0.917431
Loan balance at end of 19 years 22935.78
Interest payable in year 20 22935.78*9%
Interest payable in year 20 $2,064.22
Principal repayment in year 20 25000-2064.22
Principal repayment in year 20 22935.78

jeff jeffy answered 1 year ago
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