Question

i need help on question 3 and 4

Intro You just took out a 15-year traditional fixed-rate mortgage for $500,000 to buy a house. The interest rate is 2.4% (APR) and you have to make payments monthly Attempt 1/10 for 10 pts. Part 1 What is your monthly payment? 3310 Correct Since it's a traditional fixed-rate mortgage, the cash flows are constant and make up an annuity. We can thus use the annuity formula, solved for PMT. Monthly interest rate:r = 0.002 Number of months: N-15.12 - 180 PY - PMT 500.000.000 - PMT - 3.310 Part 2 Attempt 2/10 for 10 pts. How much of your first monthly payment goes towards paying down the outstanding balance in $)? 2310 Correct Since the initial balance is $500,000 and the monthly interest rate is 0.002, we have to pay $500,000 0.002 - $1,000 in Interest in the first month. Therefore, the remainder of the payment is principal repayment, which reduces the outstanding balance: 3.310 - 1,000 = Principal repayment Payment Interest 2,310 Part 3 Attempt 5/10 for 10 pts. What is the outstanding balance after 1 year if you have made all 12 payments on time? 480736 Try again Try again Seo solution (-4 pts.) Part 4 Attempt 2/10 for 10 pts. How much of your 19 monthly payment goes towards paying down the outstanding balance in S)? No decime Submit

Answer 1

Part 3: Outstanding Balance after payments of 12 months:

Single Payment Compound Amount Factor=SPCAF=(F/P,i,N)=(1+i)^N

i=Monthly interest rate =0.2%=0.002

N=12 months

SPCAF=(F/P,0.2%,12)=(1+0.002)^12=1.024266

FV=Future Value of Mortgage Loan after 12 months =$500,000*SPCAF

FV=500000*1.024266=$512,132.88

Uniform Series Compound Amount Factor =USCAF=(F/A,i,N)=(((1+i)^N)-1)/i

i=Monthly interest rate =0.2%=0.002

N=12 months

USCAF=(F/A,0.2%,12)=(((1+0.002)^12)-1)/0.002=12.132884

Monthly payment should be =$3310.46

FV1=Future Value of annual payments after 12 months =3310.46*USCAF

FV1=3310.46*12.132884=$40,165.43

Outstanding balance after 12 months =FV-Fv1=$512132.88-$40,165.43=$471,967.46

Outstanding Balance after one year

$471,967.46

Part4:

Outstanding Balance at end of 12 months=$471,967.46

Monthly interest =0.002

Interest for the 13^th Month =471967.46*0.002=$943.95

Amount paid for outstanding Balance =3310.46-943.95=$2366.51

Amount paid for outstanding Balance

$2,366.51