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

Answer:

The answer is "36.197%".

Explanation:

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

Formula for EMI

$\to p \times \frac{r}{n} \times [\frac{(1+\frac{r}{n})^{nt}}{(1+\frac{r}{n})^{nt} -1}]$

$= 245,000 \times \frac{0.03125}{12} \times [\frac{(1+\frac{0.03125}{12})^{12 \times 25}}{(1+\frac{0.03125}{12})^{12 \times 25} -1}]\\\\= \ 1177.81$

Formula for calculate balance after 10 years:

$\to p \times (1+\frac{r}{n})^{nt} - EMI (\frac{(1+\frac{r}{n})^{nt} -1}{\frac{r}{n}})$

$\to 245,000 \times (1+ \frac{0.03125}{12})^{10\times 12} - 1177.81 [\frac{(1+\frac{0.03125}{12})^{10\times 12} - 1}{ \frac{0.03125}{12}}]\\\\\to \ 334739.43 - \ 165,662.30\\\\\to \ 169077.13$

Total amount after 10 years:

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

calculate rate:

$= \frac{\ 95922.87}{\ 265,000} \times 100\\\\= 36.197 \%$