Question

A couple deposits $21,000 into an account earning 7% annual interest for 20 years. Calculate the future value of the investment if the interest is compounded monthly

Round your answer to the nearest cent.

Answer 1

To calculate the future value of an investment with compound interest, use the formula: A = P(1 + r/n)
`^{(nt)`. In this case, the future value of the investment is $71,172.24.

Step-by-step explanation:

To calculate the future value of an investment with compound interest, we can use the formula: A = P(1 + r/n)
`^{(nt)`, where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the couple deposits $21,000 with an annual interest rate of 7% for 20 years, compounded monthly. So P = $21,000, r = 0.07, n = 12, and t = 20.

Plugging these values into the formula, we get A = 21000(1 + 0.07/12)⁽¹²×²⁰⁾ = $71,172.24.

Therefore, the future value of the investment will be $71,172.24.

Answer 2

`~~~~~~ \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 &\$21000\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}`

`A=21000\left(1+(0.07)/(12)\right)^(12\cdot 20)\implies A=21000\left( (1207)/(1200) \right)^(240)\implies A\approx 84813.52`