Question

Fill in the table please

Answer 1

`~~~~~~ \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}`

Answer 2

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:

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`\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.