Question

You have just borrowed $260,000 to buy a condo. You will repay the loan in equal monthly payments of $2,738.38 over the next 25 years. a. What monthly interest rate are you paying on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) b. What is the APR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. What is the effective annual rate on that loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) d. What rate is the lender more likely to quote on the loan?

Answer 1

Answer:

monthly rate: 1%

APR 12%

effective rate:

r = 12.68%

It will most probably use the APR to quote the loan

Explanation:

The loan will be an ordinary annuity of 2738.38 for 25 years which present value is 260,000

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 2,738.38

time 300 (25 years x 12 month)

PV $260,000.0000

$2738.37 \times \frac{1-(1+r)^{-300} }{r} = 260,000$

We use excel or trial and error to find which rate

rate 0.009999945 = 0.01 = 1% per month

the APR will be 1% x 12 = 12%

effective rate:

$(1+0.01)^{12} = 1 + r_e$

r = 1.12682503 - = 0.1268 = 12.68%