Question

A man borrows $120,000 to buy a home. The interest rate is 4.1%, compounded monthly, and the loan period is 30 years. a) What will be the monthly payment (360 equal payments) for the life of the loan? b) What will be the effective annual interest rate, ieff ? c) How much of the first payment will be interest? d) How much of the fiftieth (50th) payment will be interest? [Try not to put problem on a spreadsheet to find answers. Instead, evaluate how much is still owed at the time evaluated; not at the beginning or end of the loan period. Then you can use the cash flow formulas (F/A, etc.).]

Answer 1

a) interest rate = 4.1%

Monthly interest rate = 4.1/12 = 0.342% = 0.00342 = r

T = 30 years

n = 30*12 = 360 periods

P = 120000

Monthly payment = P r (1+r)ⁿ/((1+r)ⁿ​​​​​​-1)

Monthly payment = (120000*0.00342)(1+0.00342)³⁶⁰/((1+0.00342)³⁶⁰-1)

Monthly payment = 581$

b) Effective annual interest rate = (1+Nominal interest rate/n)ⁿ​​​​​​-1

n = compounding period = 12

Nominal interest rate = 4.1% = 0.041

Effective annual interest rate = (1+0.041/12)¹²-1

Effective annual interest rate = 1.0418-1 = 0.0418

Effective annual interest rate = 4.18%

c) First payment = 581$

Interest =Principal* interest rate

Principal = 120000

Interest rate = 4.1%/12

Interest rate =120000*4.1%/12

Interest = 410$