Question

Straight bank loan.  Right Bank offers EAR loans of 9.15% and requires a monthly payment on all loans. What is the APR for these monthly​ loans? What is the monthly payment for a loan of ​(a​)$215,000 for 5 ​years, ​(b​ $440,000 for 14 ​years, or ​(c​) $1,050,000 for 32 ​years?

What is the APR for these monthly​ loans?

​(Round to three decimal​ places.)

Answer 1

The APR for these monthly loans is 9.425%. The monthly payment for a loan of (a) $215,000 for 5 years is approximately $4,275.62, (b) $440,000 for 14 years is around $4,913.97, and (c) $1,050,000 for 32 years is approximately $9,473.99.

Step-by-step explanation:

To find the APR for these monthly loans, we can use the formula:

APR = (1 + EAR/12)^12 - 1

Where EAR is the nominal interest rate.

In this case, the EAR is 9.15%, so the APR would be:

APR = (1 + 0.0915/12)^12 - 1

APR = 9.425%

Now, let's calculate the monthly payment for each loan:

• (a) $215,000 for 5 years: Using the formula for mortgage payments, the monthly payment would be approximately $4,275.62.
• (b) $440,000 for 14 years: The monthly payment for this loan would be around $4,913.97.
• (c) $1,050,000 for 32 years: The monthly payment for this loan would be approximately $9,473.99.

Answer 2

The APR for monthly loans when the EAR is 9.15% is approximately 8.76%, after converting the EAR to APR considering monthly compounding. Calculating the monthly payments would require using the loan amortization formula with the effective monthly interest rate.

Step-by-step explanation:

To calculate the APR from the given EAR (Effective Annual Rate) of 9.15%, we need to use the formula for converting EAR to APR when interest is compounded monthly:

`\[ \text{APR} = (1 + \text{EAR})^((1/n)) - 1 \]`

Where n is the number of compounding periods per year. In this case, n is 12 (monthly payments per year). Plugging in the values we get:

`\[ \text{APR} = (1 + 0.0915)^{(1)/(12)} - 1 \]`

To annualize this monthly rate, we multiply by 12:

APR ≈ 0.0876 or 8.76%

The APR for these loans when the EAR is 9.15% and payments are required monthly is approximately 8.76%, rounded to three decimal places.