Question

You have just borrowed $200,000 to buy a condo. You will repay the loan in equal monthly payments of $2,106.45 over the next 25 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 %

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.)

Effective annual rate%

c. What rate is the lender more likely to quote on the loan?

APR or EAR?

Answer 1

a-1 Monthly interest rate

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment=2106.45

r - rate per period=?

n - no. of periods=25*12 = 300

200000 = 2106.45*[(1-(1+r)^-300)/r]

[(1-(1+r)^-300)/r] = 200000/2106.45

= 94.9464739253

The factor [(1-(1+r)^-n)/r] is called Present Value Annuity Factor(PVAF) . From PVAF table

r = 1%

Monthly interest rate = 1.00%

a-2. What is the APR

APR = Monthly interest rate * 12

= 1*12

= 12%

b. What is the effective annual rate on that loan?

Effective Annual Rate = (1+(APR/no. of compounding per year)^no. of compounding per year-1

= (1+(.12/12))^12 -1

= (1.01)^12 - 1

= 1.12682503013-1

= 12.68%

c. What rate is the lender more likely to quote on the loan?

Lender more likely to quote APR on the loan