Question

Can you please answer question (d) 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 #5 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

Loan amount=PV=$120,000

Number of payment=n=30*12=360

Rate of interest=i=4.1%/12=0.003417

Monthly payment=PV/(P/A, 0.003417,360)=

Monthly payment=PV/(P/A, 0.003417,360)=120000/206.95434=$579.84

b) Effective interest rate=(1+monthly interest rate)^12-1=(1+0.003417)^12-1=4.178% or say 4.18%

c) Interest component in first installment=Due amount*monthly interest rate=120000*0.003417 =$410.04

Balance at the end of 49th month=120000(F/P,0.003417,49)-579.84(F/A,0.003417,49)Interest for first installmentFor calculating interest paid with 50th installment we need to find that balance at the end of 49th month which is equal to the difference of future value of loan amount and future value of installment paid at the end of 49th month.

Balance at the end of 49th month=120000*1.181910-579.84*53.241792=110957.50

Interest for 50th installment=Balance due*monthly interest rate

=110957.50*0.003417=$379.14