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Sagot :
[tex]~~~~~~ \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}\dotfill &\$300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &15 \end{cases} \\\\\\ A=300\left(1+\frac{0.05}{4}\right)^{4\cdot 15}\implies A=300(1.0125)^{60}\implies A\approx 632.15[/tex]
The investment after 15 years by the given rate of interest will be around $632.15.
What is compound interest?
Compound interest is applicable when there will be a change in principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given,
Principle amount(P) = $300
Rate of interest (R) = 5%
Time period (T) = 15 years
The compound interest formula is given by
A = P[tex][ 1 + 0.0R/n]^{nT}[/tex]
So,
A = 300 [ 1 + 0.05/4] to the power of 4(15)
A = 300[1.0125]⁶⁰
A = $632.1544 ≈ $632.15.
Hence "The investment after 15 years by the given rate of interest will be around $632.15".
For more information about compound interest
brainly.com/question/26457073
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