Question

Please answer #2 only

Ed wants to buy a property for $320,000 and wants a CPM loan for 80%. A lender indicates the loan can be obtained for 30 years at 5.5% with an origination loan fee of $1,200 and 2 points.

1. How much will the lender actually disburse?

$249,680

2. What is the effective interest cost to the borrower, assuming that the mortgage is paid after 30 years?

a. 3.79%

b. 6%

c. 5.54%

d. 5.73%

e. 5.77%

Answer 1

To calculate the effective interest cost to the borrower; first we have to calculate annual payment (PMT) on the above loan

Loan amount = 80% of the cost of property = 80% * $320,000 = $256,000

We can use PV of an Annuity formula to calculate the annual payment of loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of loan = $256,000

PMT = Annual payment =?

n = N = number of payments = 30 years

i = I/Y = interest rate per year = 5.5%

Therefore,

$256,000 = PMT* [1- (1+5.5%) ^-30]/5.5%

PMT = $17,614.18

Annual payment is $17,614.18

But we know that the actual amount of disbursement is $249,680; therefore calculate the effective interest cost to the borrower in following manner

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of loan = $249,680

PMT = Annual payment =$17,614.18

n = N = number of payments = 30 years

i = I/Y = effective interest rate per year =?

Therefore,

$249,680 = $17,614.18 * [1- (1+i) ^-30]/i

By trial and error method, we can calculate the value of i from the above equation.

Where, i= 5.73% per year

The effective interest cost to the borrower is 5.73%.

Therefore correct answer is option d. 5.73%

Or we can use excel function “RATE” to calculate the effective interest rate; where- PMT = 17,614.18, PV =249,680 FV = 0, NPER (N) = 30