Question

Compound Interest: A woman puts $2,000 in a savings account that pays 5% compounded annually. How much money is in the account at the end of 2 years?There is $ ? in the account after 2 years.

Answer 1

Formula for compound interest:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A\colon\text{ amount} \\ P\colon\text{ principal} \\ n\colon\text{ number of times interest is compound} \\ r\colon\text{interest rate (decimal)} \\ t\colon\text{time} \end{gathered}$

For the given sitiation:

P: $2,000

r: 5% = 0.05

n:1 (anually)

t: 2 years

$\begin{gathered} A=2000(1+0.05)^2 \\ \\ A=2000(1.05)^2 \\ \\ A=2000\times1.1025 \\ \\ A=2205 \end{gathered}$Then, There is $2,205 in the account after 2 years