Question

How much interest is earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded MONTHLY?

Answer 1

$2,403.02

Explanation:

To calculate the amount of interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly, we can use the compound interest formula:

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+(r)/(n)\right)^(nt)-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ interest earned. \\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}`

Given values:

• P = $12,585
• r = 3.5% = 0.035
• n = 12 (compounded monthly)
• t = 5 years

Substitute the values into the formula and solve for I:

`I=12585\left(1+(0.035)/(12)\right)^(12 \cdot 5)-12585`

`I=12585\left(1.00291666...\right)^(60)-12585`

`I=12585(1.19094282...)-12585`

`I=14988.015...-12585`

`I=2403.01550...`

`I=\$2403.02`

Therefore, the interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly is $2,403.02 (to the nearest cent).