Question

Myra took out a 20 year loan for $80,000 at an APR of 11.5% compounded monthly, approximately what would be the total cost of her loan if she paid it off 13 years early?

Answer 1

Answer:

$178251.203502$

Step-by-step explanation:

We have given:

Principal amount which is 80,000

Time which is 20 year

Rate which is 11.5%

And since, we have to find 13 years early so, time would be: 20-13=7 years.

And since, we have to find for 12 months

Hence, n=12

We have formula to calculate compound interest:

$P{1+\frac{r}{n}}^{nt}$

On substituting the values we get:

$80,000(1+\frac{0.115}{12})^{12\cdot 7}$

$\Rightarrow 80,000(1+(\frac{.115}{12}})^{84}$

On simplification we get:

$178251.203502$

Answer 2

Well, if she were to pay it 13years earlier, that means 20 - 13, or in 7years, so the monthly compounding will only apply to the 7years

thus

 $\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 80000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\to &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus 12 times} \end{array}\to &12\\ t=years\to &7 \end{cases} \\\\\\ A=80000\left(1+\frac{0.115}{12}\right)^{12\cdot 7}$