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Fill in the table please

Fill in the table please-example-1

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~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$17300\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases}


A = 17300\left(1+(0.06)/(4)\right)^(4\cdot 5) \implies A = 17300( 1.015)^(20)\implies \boxed{A \approx 23300.59} \\\\\\ \stackrel{\textit{earned interest}}{23300.59~~ - ~~17300} ~~ \approx ~~ \boxed{6000.59}

User Elyas Pourmotazedy
by
7.9k points
3 votes

Answer:

Compound future value = $23,300.59

Interest= $ 6,000.59

Explanation:

The compound future value (FV) can be calculated using the compound interest formula:


\sf FV = P \left(1 + (r)/(n)\right)^(nt)

where:

-
\sf P is the principal amount (initial investment),

-
\sf r is the annual interest rate (in decimal form),

-
\sf n is the number of times interest is compounded per year,

-
\sf t is the time the money is invested for in years.

In this case:

-
\sf P = \$17,300

-
\sf r = 0.06 (6% in decimal form)

-
\sf n = 4 (compounded quarterly)

-
\sf t = 5 years

First, calculate the compound future value (
\sf FV):


\sf FV = 17300 \left(1 + (0.06)/(4)\right)^(4 * 5)


\sf FV = 17300 \left(1 + 0.015\right)^(20)


\sf FV = 17300 * (1.015)^(20)


\sf FV \approx 17300 * 1.34685500


\sf FV \approx 23300.59 \textsf{ ( in 2 d.p.)}

So, the compound future value (
\sf FV) after 5 years is approximately $23,300.59.

Now, to find the interest earned, subtract the principal from the future value:


\sf \textsf{Interest} = FV - P


\sf \textsf{Interest} = 23,300.59 - 17300


\sf \textsf{Interest} \approx 6010.59

Therefore, the interest earned after 5 years is approximately $6,000.59.

User Jamheadart
by
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