Question

if a person invests $1,000 into an account that earns 8% which is compounded twice a year, then what will be the amounts in 2 years?

Answer 1

The compounded interest can be found by the formula

$A=P\cdot(1+\frac{r}{n})^{n\cdot t}$

where P is the initial investment, r is the rate in which the account increases in decimal form and n will be the number of coumpounding done in a year.

Replace the data into the formula.

$A=1,000\cdot(1+\frac{0.08}{2})^{2\cdot t}$

find the amount in 2 years, by giving t the value of 2.

$\begin{gathered} A=1,000\cdot(1+\frac{0.08}{2})^{2\cdot2} \\ A=1,000\cdot(1.04)^4 \\ A\cong1169.86 \end{gathered}$