. A borrower is purchasing a property for $300,000 and can choose between two po
ID: 2777376 • Letter: #
Question
. A borrower is purchasing a property for $300,000 and can choose between two possible loan alternatives. The first is a 90% loan for 20 years at 6.0% interest and the second is an 80% loan for 20 years at 5.0% interest. Assume the loan will be held to maturity. What is the incremental interest cost of borrowing the extra money?
Loan 1 Loan 2
Loan to value ratio 90% 80%
Interest rate 6.0% 5.0%
Term 20 years 20 years
Please provide Explanation and how you did this using a financial calculator
Explanation / Answer
Loan 1
Loan amount PV = 300,000x90% = 270,000
N = 20x12 = 240
R= 6%/12 = 0.5%
FV=0
We need to solve for Pmt to get monthly payment amount. Please remember to enter PV with negative sign.
Pmt= 1934.36
Loan 2
Loan amount PV = 300,000x80% = 240,000
N = 20x12 = 240
R= 5%/12 = 0.41667%
FV=0
We need to solve for Pmt to get monthly payment amount. Please remember to enter PV with negative sign.
Pmt= 1583.89
Incremental loan amount = 270,000 -240,000
= 30,000
Incremental Pmt = 1934.36 - 1583.89
= 350.47
Now we need to solve for rate using the following inputs:
PV= 30,000
Nper = 20x12 =240
Pmt = -350.47
P/Y =12
C/Y =12
Solve for rate, you will get = 12.95%
Therefore 12.95% is the incremental cost of borrowing the extra money.
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