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

The monthly interest rate on the loan is approximately 1.05%, the APR is approximately 12.61%, and the effective annual rate is approximately 13.22%. The lender is more likely to quote the APR on the loan.

Step-by-step explanation:

To find the monthly interest rate on the loan, we need to calculate the interest rate expressed as a monthly fraction. We can do this by using the formula:

Interest Rate (as a decimal) = (Monthly Payment / Loan Amount) - 1

In this case, the monthly payment is $2,738.38 and the loan amount is $260,000. Plugging in these values, we get:

Interest Rate (as a decimal) = (2738.38 / 260000) - 1 = 0.01053661538

Multiplying by 100 to convert to percentage, the monthly interest rate is approximately 1.05%.

To find the APR, we can use the monthly interest rate calculated above and multiply it by 12 to get the annual interest rate. In this case, the APR is approximately 12.61%.

The effective annual rate (EAR) takes into account any compounding that occurs during the year. To calculate the EAR, we can use the formula:

EAR = (1 + Monthly Interest Rate)¹² - 1

Plugging in the monthly interest rate of 0.01053661538, we get:

EAR = (1 + 0.01053661538)¹² - 1 = 0.13220464496

Multiplying by 100 to convert to percentage, the EAR is approximately 13.22%.

The lender is more likely to quote the APR on the loan as it is a standardized measure that can be compared across different loan options.

Answer 2

monthly rate: 1%

APR 12%

effective rate:

r = 12.68%

It will most probably use the APR to quote the loan

Step-by-step explanation:

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

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 2,738.38

time 300 (25 years x 12 month)

PV $260,000.0000

`2738.37 * (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%