Question

calculate the future value of $835 at 3.5% compounded semiannually for 6years​

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 835\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &6 \end{cases} \\\\\\ A=835\left(1+\frac{0.035}{2}\right)^{2\cdot 6}\implies A=835(1.0175)^{12}\implies A\approx 1028.25$

Answer 2

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;

$\rm Future \ value =P\left ( 1+\dfrac{r}{n}\right)^{nt}$

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

$\rm Future \ value =P\left ( 1+\dfrac{r}{n}\right)^{nt}\\\\\rm Future \ value =835\left ( 1+\dfrac{0.035}{2}\right)^{2\times 6}\\\\ Future \ value =835 ( 1.0175)^{12}\\\\ Future \ value =835\times 1.23\\\\ Future \ value =1028.25$

Hence, the future value of $835 at 3.5% compounded semiannually for 6 years​ is $1028.25.

Learn more about compound interest here;

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