Respuesta :
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
[tex]\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}[/tex]
thus
[tex]\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}[/tex]
Answer:
[tex]178251.203502[/tex]
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:
[tex]P{1+\frac{r}{n}}^{nt}[/tex]
On substituting the values we get:
[tex]80,000(1+\frac{0.115}{12})^{12\cdot 7}[/tex]
[tex]\Rightarrow 80,000(1+(\frac{.115}{12}})^{84}[/tex]
On simplification we get:
[tex]178251.203502[/tex]
