Question

(50 points) Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded monthly until the end of August.

Answer 1

$9,712.12 (nearest cent)

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 = $9,544
• r = 5.25% = 0.0525
• n = 12 (monthly)
• t = 4 months = 1/3 year

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

`\implies A=9544\left(1+(0.0525)/(12)\right)^{12 \cdot (1)/(3)}`

`\implies A=9544\left(1.004375\right)^(4)`

`\implies A=9544\left(1.017615179\right)`

`\implies A=9712.119269`

The balance of the account at the end of August will be $9,712.12 (nearest cent).