Question

Cheryl invests $1000 into a savings account with a 3% interest rate. Howmuch money will she have if her money is compounded quarterly for 20years?

Answer 1

The formula to calculate the final amount after a compound interest period is given as

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

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

From the question, we have

P = 1000

r = 3% = 0.03

n = 4 (quarterly)

t = 20

Substituting into the formula, we have

$\begin{gathered} A=1000(1+\frac{0.03}{4})^{4\times20} \\ A=1000(\frac{403}{400})^{80} \\ A=1000\times1.818 \\ A=1818.04 \end{gathered}$

Therefore, the money she has after the period is $1818.04.