Question

What would be your mortgage payment if you pay for a $250,000 home by making a 20% down payment and then taking out a 3.74% thirty year fixed rate mortgage loan to cover the remaining balance

Answer 1

Answer:

$925.097.                    

Step-by-step explanation:

We  will use EMI formula to answer our problem.

$E=P\cdot r\cdot \frac{(1+r)^{n}}{((1+r)^{n}-1)}$, where,

E is EMI.

P= Principal loan amount.

r= the rate of interest calculated on monthly basis.

We need to figure out our principal loan amount before using this formula. We are told that we have to pay 20% of $250,000 as down payment, therefore our principal loan amount will be 80% of $250,000.

$\text{Principal loan amount}=\frac{80}{100} \times 250,000$

$\text{Principal loan amount}=0.80 \times 250,000=200000$

$r=\frac{0.0374}{12} =0.0031166666666667$

Now let us use EMI formula to find our mortgage payment.

$E=200,000\cdot 0.0031166666666667\cdot \frac{(1+0.0031166666666667)^{(30*12)}}{((1+0.0031166666666667)^{(30*12)}-1)}$            

$E=623.33333333334\cdot \frac{(1.0031166666666667)^{(360)}}{((1.0031166666666667)^{(360)}-1)}$

$E=623.33333333334\cdot \frac{3.0656363754770338961}{3.0656363754770338961-1)}$

$E=623.33333333334\cdot \frac{3.0656363754770338961}{2.0656363754770338961}$

$E=623.33333333334\cdot 1.4841123112818256882213$

$E=925.0966740323479\approx 925.097$

Therefore, the mortgage payment to cover remaining balance in 30 years will be $925.097 per month.