Question

Ms. Tweeter is buying a house with a cost of $350,000. She will make a down payment of $20,000 on the house, and the rest will be paid for with a mortgage loan. Her mortgage loan has an APR of 4.9% compounded semi-annually, with a weekly payment schedule and a time horizon of 20 years. The first payment is due in one week's time. How much principal have you paid off after 5 years?

Answer 1

Principal you have paid off after 5 years = $ 55336.88

Explanation:

Weekly rate = (1+APR/2)^(2/52)-1

Weekly rate = (1+4.9%/2)^(2/52)-1

Weekly rate = 0.0931383%

Weekly Payment = Loan Amount/((1-(1+r)^-n)/r)

• r = 0.0931383%
• n = 20*52 = 1040

Weekly Payment = (350000-20000)/((1-(1+0.0931383%)^-1040)/0.0931383%)

Weekly Payment = 495.55

Loan Amount outstanding after 5 year = Weekly Payment*((1-(1+r)^-n)/r)

• r = 0.0931383%
• n = 20*52 - 5*52 = 780

Loan Amount outstanding after 5 year =495.55*((1-(1+0.0931383%)^-780)/0.0931383%)

Loan Amount outstanding after 5 year = 274663.12

Principal you have paid off after 5 years = Loan Amount-Loan Amount outstanding after 5 year

Principal you have paid off after 5 years = 330000- 274663.12

Principal you have paid off after 5 years = 55336.88

I hope this clear your doubt.

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