Say you bought a house for $275,000 with 10% down, and financed it from a bank f

Question

Say you bought a house for $275,000 with 10% down, and financed it from a bank for a 30-year term at 4.75% interest per year compounded monthly. If you paid an extra $1,000 every year (end of 12th month) along with the regular month-end payments, which will be true from the following?

You will be able to cut off 42 full payments and a partial payment from the loan.

You will have to make only 315 payments.

You will have to make 316 payments of $1,291.08 each, pay $1,000 at the end of the first 26 years, & make a 317th payment of $1,194.97.

You will have to make 316 paymnents of $1,291.08 each & make a 317th payment of $1,190.26.

You will be able to cut off 42 full payments and a partial payment from the loan.

You will have to make only 315 payments.

You will have to make 316 payments of $1,291.08 each, pay $1,000 at the end of the first 26 years, & make a 317th payment of $1,194.97.

You will have to make 316 paymnents of $1,291.08 each & make a 317th payment of $1,190.26.

Explanation / Answer

Option D

Let monthly payments be x

0=-275000*(1-10%)+x/(1+0.0475/12)+x/(1+0.0475/12)^2.............

0=-247500+x/(1+0.0475/12)*(1-1/(1+0.0475/12)^360)/(1-1/(1+0.0475/12))

hence, x=247500/(1-1/(1+0.0475/12)^360)*0.0475/12

x=1291.08

So, monthly payments=1291.08 each

If additional 1000 is paid each year at the end of the year:

0=-247500+1291.08/(1+0.0475/12)*(1-1/(1+0.0475/12)^(12*n))/(1-1/(1+0.0475/12))+1000/((1+0.0475/12)^12)*(1-1/(1+0.0475/12)^(12*k))/(1-1/(1+0.0475/12)^12)

Total 316 full payments of 1291.08 and one partial payment of 1190.26 and 26 payments of 1000

Option C is incorrect because of the 317th payment incorrectly mentioned

Option B is incorrect because of incorrect number of payments mentioned

Option A is incorrect because you will be able to cut off 43 full payments and one partial repayment

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