Question

Can someone help me with this question????

Answer 1

`P = \boxed{\sf 4000}`

`r=\boxed{\sf 0.03}`

`n=\boxed{\sf 4}`

`t=\boxed{\sf 5}`

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+(r)/(n)\right)^(nt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

If you invest $4,000 then the principal amount is $4,000. As P represents the principal amount:

`\implies P = \boxed{\sf 4000}`

The interest is 3%. 3% = 3/100 = 0.03. Therefore:

`\implies r=\boxed{\sf 0.03}`

"n" represents the number of times interest is applied per year.

Therefore, if the interest is applied quarterly then:

`\implies n=\boxed{\sf 4}`

"t" represents the time in years. Therefore, if you plan to leave the money in the account for 5 years then:

`\implies t=\boxed{\sf 5}`

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To calculate the amount in the account after 5 years, substitute the values into the formula and solve for A:

`\implies A=4000\left(1+(0.03)/(4)\right)^(4 * 5)`

`\implies A=4000\left(1+0.0075\right)^(20)`

`\implies A=4000\left(1.0075\right)^(20)`

`\implies A=4000(1.16118414...)`

`\implies A=\$4644.74`