Question

Suppose that you are considering a loan in which you will borrow $245,000 using a 30-year loan. The loan has an annual interest rate of 6% with monthly payments and monthly compounding. Suppose also that the lender is charging you a 0.75% origination fee, you are paying 2.25 points in order to get the 6% interest rate, and the loan has $1,275 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 7th year?

Answer 1

Loan Amount=$245000

Tenure= 30 year loan.

Annual interest rate of 6% with monthly payments and monthly compounding.

Lender is charging 0.75% origination fee,

Paying 2.25 points in order to get the 6% interest rate,

Loan has $1275 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 + $1275+ 0.75% of 275000= 245000*FV(0.5%,360) + 1275 + 1837.5 = 1475530.93 + 1275 + 1837.5 =$ 1478643.43

b. What will the lender’s yield be for this loan if you make all of the scheduled payments?

=$ 1478643.43 - $ 245,000 = 1233643.43$

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= 245000*FV(0.5%,84) +1275 + 1837.5 - 245000 = 372490.5 + 3112.5 - 245000 = 130603

The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)

Where:

A = the future value of the investment
P = the principal investment amount
r = the annual interest rate
n = the number of times that interest is compounded 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 interestplus the principal. Should you wish to calculate the compound interest only, you need this:

Total compounded interest = P (1 + r/n) (nt) - P