Question

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3400 dollars is placed in an account with an annual interest rate of 8.25%. how much will be in the account after 25 years, to the nearest cent?
answer attempt 1 out of 2
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Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year. (Assuming it's compounded annually, so $n = 1$)
• $t$ is the time the money is invested for in years.

Given:

• $P = 3400$ dollars
• $r = 8.25\% = 0.0825$ (converted to decimal)
• $n = 1$ (annual compounding)
• $t = 25$ years

Step2: Substitute the values into the formula

Substitute $P = 3400$, $r = 0.0825$, $n = 1$, and $t = 25$ into the formula:

$A = 3400(1 + \frac{0.0825}{1})^{1 \times 25}$

Simplify the expression inside the parentheses first:

$1 + \frac{0.0825}{1} = 1.0825$

Then calculate the exponent:

$1 \times 25 = 25$

So now we have:

$A = 3400(1.0825)^{25}$

Step3: Calculate $(1.0825)^{25}$

Using a calculator, $(1.0825)^{25} \approx 6.84847$

Step4: Multiply by the principal amount

$A = 3400 \times 6.84847$

Calculate this product:

$3400 \times 6.84847 \approx 23284.80$ (rounded to the nearest cent)

Answer:

23284.80