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 &\$835\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &6 \end{cases} \\\\\\ A=835\left(1+\frac{0.035}{2}\right)^{2\cdot 6}\implies A=835(1.0175)^{12}\implies A\approx 1028.25[/tex]
The future value of $835 at 3.5% compounded semiannually for 6 years is $1028.25.
What is the compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
The future value of $835 at 3.5% compounded semiannually for 6 years.
The future value is given by;
The effective rate for a rate r compounded m times per period;
[tex]\rm Future \ value =P\left ( 1+\dfrac{r}{n}\right)^{nt}[/tex]
Where; Present value = $835
Interest rate (r) = 3.5%
n = 2
T = Time duration in years = 6 years
Substitute all the values in the formula
[tex]\rm Future \ value =P\left ( 1+\dfrac{r}{n}\right)^{nt}\\\\\rm Future \ value =835\left ( 1+\dfrac{0.035}{2}\right)^{2\times 6}\\\\ Future \ value =835 ( 1.0175)^{12}\\\\ Future \ value =835\times 1.23\\\\ Future \ value =1028.25[/tex]
Hence, the future value of $835 at 3.5% compounded semiannually for 6 years is $1028.25.
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