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antiseptic1488 [7]
3 years ago
15

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 he

r loan if she paid it off 13 years early?
Mathematics
2 answers:
Mkey [24]3 years ago
5 0

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

antoniya [11.8K]3 years ago
5 0
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}
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