Question

You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loan’s EFF%?

Answer 1

The monthly loan payment for a $20,000 car loan with a 12% interest rate over 5 years is approximately $424.55. The loan's EFF% is approximately 12.68%.

Step-by-step explanation:

To find the monthly loan payment, we can use the formula for the amortization of a loan:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^-Total Months)

For this loan, the loan amount is $20,000, the monthly interest rate is 12% divided by 12 months (0.12 / 12 = 0.01), and the total months are 60. Plugging in these values, we get:

Monthly Payment = (20000 * 0.01) / (1 - (1 + 0.01)^-60)

Simplifying the equation and calculating, the monthly loan payment is approximately $424.55.

To find the loan's EFF%, we can use the formula:

EFF% = (1 + Monthly Interest Rate)^12 - 1

For this loan, the monthly interest rate is 0.12 divided by 12 (0.12 / 12 = 0.01). Plugging in this value, we get:

EFF% = (1 + 0.01)^12 - 1

Calculating, the loan's EFF% is approximately 12.68%.

Answer 2

1) Monthly loan payment = $445

2) EFF% = 12.6%

Step-by-step explanation:

1) In order to find the monthly payment we need to have future value, present value, interest rate and number of periods

Present value = $20,000

Future value = 0 (because fully amortized loan means no lump sum payment at the end of the loan)

Interest = 12/12= 1 (we divide by interest rate by 12 because we are given a yearly interest rate but we have to find monthly payments so we have to compound interest monthly)

N= 5*12= 60 ( because there are monthly payments there will be a total of 60 payments through out the time period of the loan)

Put these values in a financial calculator and compute PMT

PMT= 445

2) EFF. In order to find the effective interest rate we need to find how the compounding each month affect the interest rate so the formula for that is

((1+I/N)^N)-1

I is the yearly interest rate which is 12%

N is the number of compounding periods in a year which are 12 as there are 12 months in a year

=((1+0.12/12)^12)-1=0.126= 12.6%