You want to buy a car, and a local bank will lend you $15,000. The loan would be fully amortized over 4 years (48 months), and the nominal interest rate would be 15%, with interest paid monthly.
1A) What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.
1B) What is the loan's EFF%? Do not round intermediate calculations. Round your answer to two decimal places.
(1)(A)-The Monthly Loan Payment
Loan Amount (P) = $15,000
Monthly interest rate (n) = 1.25% per month [12.00% / 12 Months]
Number of period (n) = 48 Months [4 Years x 12 Months]
Therefore, the Monthly Loan Payment = [P x {r (1 + r)n} ] / [(1 + r)n – 1]
= [$15,000 x {0.0125 x (1 + 0.0125)48}] / [(1 + 0.0125)48 – 1]
= [$15,000 x {0.0125 x 1.815354853}] / [1.815354853 – 1]
= [$15,000 x 0.022691936] / 0.815354853
= $340.38 / 0.815354853
= $417.46 per month
(1)(B)-Effective Annual Rate (EFF)
Effective Interest Rate (EAR) is calculated by using the following formula
Effective Interest Rate = [1 + (r/ n)] n − 1
Where, annual interest rate (r) = 12.00% per year
Number of compounding period (n) = 12 Months
Therefore, the Effective Interest Rate (EAR) = [1 + (r/ n)] n − 1
= [1 + (0.12/12)]12 – 1
= [1 + 0.0125]12 – 1
= 1.160754518 – 1
= 0.160754518 or
= 16.08% (Rounded to 2 decimal place)
You want to buy a car, and a local bank will lend you $15,000. The loan...
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