You have just borrowed $120,000 to buy a condo. You will repay the loan in equal

Question

You have just borrowed $120,000 to buy a condo. You will repay the loan in equal monthly payments of $1,580.15 over the next 20 years. a-1. What monthly interest rate are you paying on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Monthly interest rate t a-2. What is the APR? (Do not round intermediate calculations. Enter your answer as a whole percent.) APR b. What is the effective annual rate on that loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Explanation / Answer

Amount borrowed = $120,000
Monthly payment = $1,580.15
Period = 20 years or 240 months

Let monthly interest rate be i%

$120,000 = $1,580.15 * PVIFA(i%, 240)

Using financial calculator:
N = 240
PV = -120000
PMT = 1580.15
FV = 0

I = 1.25%

Monthly Interest Rate = 1.25%

Annual Interest Rate = 12 * 1.25%
Annual Interest Rate = 15%

Effective Annual Rate = (1 + Monthly Interest Rate)^12 - 1
Effective Annual Rate = (1 + 0.0125)^12 - 1
Effective Annual Rate = 1.0125^12 - 1
Effective Annual Rate = 1.1608 - 1
Effective Annual Rate = 0.1608 or 16.08%

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