ABC Bank sanctions a loan application for a 25 year mortage loan for US100,000. The interest...

ABC Bank sanctions a loan application for a 25 year mortage loan for US100,000. The interest rate on the loan is 12% per annum and the borrower is required to make equal monthly payments to repay the loan in 25 years. If the market interest rate goes down to 10% per annum, what will the loan be worth? (Answer up to two decimal places,

Expert Solution

Loan = $100000, Initial interest rate = 12% per annum, Period of loan = 25 years = 25 x 12 months = 300 months

Initial monthly rate = Initial interest rate / 12 = 12%/12 = 1% per month

First we will need to find the equal monthly payment of loan at initial monthly rate

We can find the equal monthly payment of loan at initial monthly rate by using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get Equal Monthly payment of loan = $1053.22

Now if the interest rate changes to 10% per annum

then New monthly rate = New per annum interest rate / 12 = 10%/12

We know the value or worth of loan is equal to present value of equal monthly monthly loan payments discounted at current monthly interest rate

We can find the present value of equal monthly payments or worth of loan by using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel ,we get worth of loan = 115903.9436 = $115903.94

Hence if interest rate goes down to 10% per annum, then worth of loan = 115903.94

jeff jeffy answered 9 months ago

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