Question

Alyson deposits $500 in the bank for 12 years. The bank offers her a 4% interest rate compounded monthly. How much money will be in her account at the end

of the 12 years? (Remember to round your answer to the nearest cent.)

Answer 1

$807.39

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+(r)/(n)\right)^(nt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \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:

• P = $500
• r = 4% = 0.04
• n = 12 (monthly)
• t = 12 years

Substitute the given values into the compound interest formula and solve for A:

`\implies A=500\left(1+(0.04)/(12)\right)^(12 \cdot 12)`

`\implies A=500\left(1.00333333...\right)^(144)`

`\implies A=500\left(1.61478492...\right)`

`\implies A=807.392461...`

Therefore, Alyson will have $807.39 (nearest cent) in her account at the end of 12 years.