You want to buy a new sports coupe for $75,400, and the finance office at the de

ID: 2751357 • Letter: Y

Question

You want to buy a new sports coupe for $75,400, and the finance office at the dealership has quoted you a loan with an APR of 7.8 percent for 60 months to buy the car.

What will your monthly payments be? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

What is the effective annual rate on this loan? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

You want to buy a new sports coupe for $75,400, and the finance office at the dealership has quoted you a loan with an APR of 7.8 percent for 60 months to buy the car.

Explanation / Answer

r is rate of interest calculated on monthly basis. (i.e., r = Rate of Annual interest/12/100. If rate of interest is 10.5% per annum, then r = 10.5/12/100=0.65)

For example, if you borrow $10,00,000 from the bank at 10.5% annual interest for a period of 10 years (i.e., 120 months), then EMI = S10,00,000 * 0.65 * (1 + 0.65)120 / ((1 + 0.65)120 – 1) = $13,493. i.e., you will have to pay $13,493 for 120 months to repay the entire loan amount. The total amount payable will be $13,493 * 120 = S16,19,220 that includes $6,19,220 as interest toward the loan.

r is rate of interest calculated on monthly basis. (i.e., r = Rate of Annual interest/12/100. If rate of interest is 7.8% per annum, then r = 7.8/12/100=0.650.65

borrow $75,400 from the bank at 7.8% annual interest for a period of 60 months

then EMI = S75,400 x 0.0065 x(1 + 0.0065)60 / ((1 + 0.0065)60 – 1) = $13,493.

=$490.01 x 1.47512/0.47512=$490.01 x 3.10473=$1521.34

i.e., you will have to pay $1521.34

for 60 months to repay the entire loan amount.

The total amount payable will be $1521.34 * 60 = S91,280.4that includes $ 15,901.84 as interest toward the loan.

Monthly Payment= $1521.34

Effective Annual Interest Rate

r=(1+i/n)n-1

=(1+0.05/60)60-1=8.11%

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