Suppose that you are considering a loan in which you will borrow $275,000 using
ID: 2782477 • Letter: S
Question
Suppose that you are considering a loan in which you will borrow $275,000 using a 30-year loan. The loan has an annual interest rate of 15% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 0.75% origination fee, you are paying 3 points in order to get the 15% interest rate, and the loan has $675 in third-party closing costs associated with it. a. What will the effective borrowing cost be for this loan if you make all of the scheduled payment? b. What will the lender’s yield be for this loan if you make all of the scheduled payments? c. What will the effective borrowing cost be for this loan if you pay off the loan at the end of the 4th year?
Explanation / Answer
Loan Amount=$275,000
Tenure= 30 year loan.
Annual interest rate of 15% with monthly payments and monthly compounding.
Lender is charging 0.75% origination fee,
Paying 3 points in order to get the 15% interest rate,
Loan has $675 in third-party closing costs associated with it.
a. What will the effective borrowing cost be for this loan if you make all of the scheduled payment?
Total Installments + $675+ 0.75% of 275000=24,073,773.66+675+20625=$ 24,095,073.66
b. What will the lender’s yield be for this loan if you make all of the scheduled payments?
=$ 24,095,073.66- $ 275,000
c. What will the effective borrowing cost be for this loan if you pay off the loan at the end of the 4th year?
Ans= $ 499,222.58
The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Note that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. Should you wish to calculate the compound interest only, you need this:
Total compounded interest = P (1 + r/n) (nt) - P
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