Question

question 13
kadesha invested $8850 in an account paying an interest rate of 2.15% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 17 years?
answer
$

Explanation:

Step1: Recall compound interest formula

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.
• $t$ is the time the money is invested for in years.

In this problem, $P = 8850$, $r = 2.15\% = 0.0215$, $n = 1$ (compounded annually), and $t = 17$.

Step2: Substitute values into the formula

Substitute the given values into the formula:
$A = 8850(1 + \frac{0.0215}{1})^{1 \times 17}$
Simplify the expression inside the parentheses: $1 + 0.0215 = 1.0215$
Then, calculate the exponent: $1 \times 17 = 17$
So, $A = 8850(1.0215)^{17}$

Step3: Calculate $(1.0215)^{17}$

Using a calculator, $(1.0215)^{17} \approx 1.0215^{17} \approx 1.4203$ (rounded to four decimal places)

Step4: Calculate $A$

Multiply the principal by the calculated value:
$A = 8850 \times 1.4203$
$A \approx 8850 \times 1.4203 \approx 12569.655$

Step5: Round to the nearest dollar

Rounding $12569.655$ to the nearest dollar gives $12570$.

Answer:

12570