Question

Help with finding answers to investment word problemsNatalie invests $5,000 into a savings account which earns 10% per year. In 5 years how much will Natalie’s investment be worth if interest is compounded quarterly

Answer 1

Answer

$8,193.08

Step-by-step explanation

Compound interest formula

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

where

• A: final amount

,

• P: principal (initial amount)

,

• r: interest rate, as a decimal

,

• n: number of times interest is applied per year

,

• t: time in years

Substituting P = $5,000, r = 0.1 ( = 10/100), n = 4 (quarterly means 4 times per year), and t = 5 years, we get:

$\begin{gathered} A=5,000\cdot(1+\frac{0.1}{4})^{4\cdot5} \\ A=5,000\operatorname{\cdot}(1.025)^{20} \\ A=\text{ \ }8,193.08 \end{gathered}$