Respuesta :
[tex]\bf ~~~~~~ \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 &\$7000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &22 \end{cases} \\\\\\ A=7000\left(1+\frac{0.07}{1}\right)^{1\cdot 22}\implies A=7000(1.07)^{22}\implies A\approx 31012.81[/tex]
The compound interest at the end of 22 years is $31,012.81
Compound Interest
To solve this question, we need to use the formula of compound interest.
This is given as
[tex]A = P(1 + (\frac{r}{n}))^n^t[/tex]
- A = interest compounded
- P = principal of the investment = $7000
- r = rate = 7% = 0.07
- n = number of times compounded = 1
- t = time = 22 years
substituting the values into the equation above, we would have;
[tex]A = 7000(1 + \frac{0.07}{1})^1^*^2^2\\A = 7000(1+0.07)^2^2\\A = 7000*1.07^2^2\\A = 31,012.81[/tex]
Lane's interest compounded at the rate of 7% for 22 years is $31,012.81
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