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kotegsom [21]
3 years ago
12

A person invests $4000 at 2% interest compounded annually for 4 years and then invests the balance (the $4000 plus the interest

earned) in an account at 8% interest for 7 years. Find the value of the investment after 11 years.
(Hint: You need to break this up into two steps/calculations. Be sure to round your balance at the end of the first 4 years to the nearest penny so you can use it in the second set of calculations.)
Mathematics
1 answer:
faltersainse [42]3 years ago
7 0
\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$4000\\
r=rate\to 2\%\to \frac{2}{100}\to &0.02\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &4
\end{cases}
\\\\\\
A=4000\left(1+\frac{0.02}{1}\right)^{1\cdot 4}\implies A=4000(1.02)^4\implies A\approx 4329.73

then she turns around and grabs those 4329.73 and put them in an account getting 8% APR I assume, so is annual compounding, for 7 years.

\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$4329.73\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &7
\end{cases}
\\\\\\
A=4329.73\left(1+\frac{0.08}{1}\right)^{1\cdot 7}\implies A=4329.73(1.08)^7\\\\\\ A\approx 7420.396

add both amounts, and that's her investment for the 11 years.
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<h3>Answer:</h3>

System

  • p + m = 10
  • 0.8m = 0.4·10

Solution

  • p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>Step-by-step explanation:</h3>

(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.

For the total amount of mix:

... p + m = 10

For the quantity of peanuts in the mix:

... p + 0.2m = 0.6·10

For the quantity of almonds in the mix:

... 0.8m = 0.4·10

For the ratio of peanuts to almonds:

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Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.

So, your system of equations could be ...

  • p + m = 10
  • 0.8m = 0.4·10

___

(b) Dividing the second equation by 0.8 gives

... m = 5

Using the first equation to find p, we have ...

... p + 5 = 10

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