Question

After 10 years of regular monthly payments on a 25-year amortized loan for $245,000 at 3.125% interest compounded monthly, how much equity do they have in the house, assuming a $20,000 down-payment (on a $265,000 home)

Answer 1

The answer is "36.197%".

Step-by-step explanation:

`p = \$ 245,000 \\\\r= 3.125\% = 0.03125\\\\n=12 \\\\t= 25 \ years\\\\`

Formula for EMI

`\to p * (r)/(n) * [((1+(r)/(n))^(nt))/((1+(r)/(n))^(nt) -1)]`

`= 245,000 * (0.03125)/(12) * [((1+(0.03125)/(12))^(12 * 25))/((1+(0.03125)/(12))^(12 * 25) -1)]\\\\= \$ 1177.81\\\\`

Formula for calculate balance after 10 years:

`\to p * (1+(r)/(n))^(nt) - EMI (((1+(r)/(n))^(nt) -1)/((r)/(n)))`

`\to 245,000 * (1+ (0.03125)/(12))^(10* 12) - 1177.81 [((1+(0.03125)/(12))^(10* 12) - 1)/( (0.03125)/(12))]\\\\\to \$ 334739.43 - \$ 165,662.30\\\\\to \$ 169077.13`

Total amount after 10 years:

`\to \$265000 -\$169077.13\\\\\to \$ 95922.87`

calculate rate:

`= (\$ 95922.87)/(\$ 265,000) * 100\\\\= 36.197 \%`