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

$925.097.

Explanation:

We will use EMI formula to answer our problem.

`E=P\cdot r\cdot ((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}=(80)/(100) * 250,000`

`\text{Principal loan amount}=0.80 * 250,000=200000`

`r=(0.0374)/(12) =0.0031166666666667`

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

`E=200,000\cdot 0.0031166666666667\cdot ((1+0.0031166666666667)^((30*12)))/(((1+0.0031166666666667)^((30*12))-1))`

`E=623.33333333334\cdot ((1.0031166666666667)^((360)))/(((1.0031166666666667)^((360))-1))`

`E=623.33333333334\cdot (3.0656363754770338961)/(3.0656363754770338961-1))`

`E=623.33333333334\cdot (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.