Answer:
$291,016.80
A is correct.
Step-by-step explanation:
You are applying for an 80/20 mortgage to buy a house costing $145,000.
Loan Formula:
![EMI=\dfrac{P\cdot r}{1-(1+r)^{-n}}](https://tex.z-dn.net/?f=EMI%3D%5Cdfrac%7BP%5Ccdot%20r%7D%7B1-%281%2Br%29%5E%7B-n%7D%7D)
Case 1:
Loan amount, P = 80% of 145000 = $ 116,000
Rate of interest, r = 4.75% = 0.0475
Time of loan, n = 30 years = 360 months
Substitute the values into formula.
![EMI=\dfrac{116000\cdot \frac{0.0475}{12}}{1-(1+\frac{0.0475}{12})^{-360}}](https://tex.z-dn.net/?f=EMI%3D%5Cdfrac%7B116000%5Ccdot%20%5Cfrac%7B0.0475%7D%7B12%7D%7D%7B1-%281%2B%5Cfrac%7B0.0475%7D%7B12%7D%29%5E%7B-360%7D%7D)
![EMI=605.11](https://tex.z-dn.net/?f=EMI%3D605.11)
Total payment for case 1: 605.11 x 360 = $217,839.60
Case 2:
Loan amount, P = 20% of 145000 = $ 29,000
Rate of interest, r = 4.75% = 0.07525
Time of loan, n = 30 years = 360 months
Substitute the values into formula.
![EMI=\dfrac{29000\cdot \frac{0.07525}{12}}{1-(1+\frac{0.07525}{12})^{-360}}](https://tex.z-dn.net/?f=EMI%3D%5Cdfrac%7B29000%5Ccdot%20%5Cfrac%7B0.07525%7D%7B12%7D%7D%7B1-%281%2B%5Cfrac%7B0.07525%7D%7B12%7D%29%5E%7B-360%7D%7D)
![EMI=203.27](https://tex.z-dn.net/?f=EMI%3D203.27)
Total payment for case 1: 203.27 x 360 = $73,177.20
Total amount of the mortgage = $217,839.60 + $73,177.20
= $291,016.80
Hence, The total amount of the mortgage is $291,016.80