Say you bought a house for $275,000 with 10% down, and financed it from a bank f
ID: 2784536 • Letter: S
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