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%?

1) Monthly loan payment = $445

2) EFF% = 12.6%

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%

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