Question

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Answer 1

The amount in the account for the given principal, interest rate, time and compounding period is $6,927.01 to the 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 values:

• Principal (P) = $3,960
• interest rate (r) = 3.5% = 0.035
• Compounding period (n) = 12 (monthly)
• Time (t) = 16 years

As the interest is compounded monthly, n = 12.

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

`\implies A=3960\left(1+(0.035)/(12)\right)^(12 \cdot 16)`

`\implies A=3960\left(1.00291666...\right)^(192)`

`\implies A=3960(1.7492461...)`

`\implies A=6927.01471...`

Therefore, the amount in the account for the given principal, interest rate, time and compounding period is $6,927.01 to the nearest cent.