Answer
(a) $2,240.00
(b) $2,508.80
Step-by-step explanation
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{^{nt}}[/tex]where
• A: final amount, in dollars
,• P: principal, in dollars
,• r: interest rate, as a decimal
,• n: number of times interest is applied per year
,• t: time in years
(a) Substituting into the formula with P = $2000, r = 0.12 (= 12/100), n = 1 (interest is applied once per year), and t = 1 year, we get:
[tex]\begin{gathered} A=2000(1+\frac{0.12}{1})^{1\cdot1} \\ A=2,000(1.12) \\ A=\text{ \$}2240 \end{gathered}[/tex](b) Substituting the same values as item a, except t = 2 years, we get:
[tex]\begin{gathered} A=2,000(1+\frac{0.12}{1})^{1\cdot2} \\ A=2,000(1.12)^2 \\ A=\text{ \$}2508.80 \end{gathered}[/tex]