Question

gavin opened a savings account with a principal balance of $2,250 and will not make any additional deposits or withdrawals. the account earns 2.4% interest compounded annually. what is the total amount that gavin will have in his account at the end of 6 years?

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, since it's compounded annually, $n = 1$, $P=\$2250$, $r = 2.4\%=0.024$, and $t = 6$ years.

Step2: Substitute values into the formula

Substitute $P = 2250$, $r=0.024$, $n = 1$, and $t = 6$ into the formula:
$A=2250(1+\frac{0.024}{1})^{1\times6}$

Step3: Simplify the expression

First, calculate the value inside the parentheses: $1+\frac{0.024}{1}=1.024$
Then, calculate the exponent: $1\times6 = 6$
So we have $A = 2250\times(1.024)^{6}$

Now, calculate $(1.024)^{6}$. Using a calculator, $(1.024)^{6}\approx1.15438$.

Then, multiply by the principal: $A=2250\times1.15438\approx2250\times1.1544$ (rounding for easier calculation)
$2250\times1.1544 = 2250\times(1 + 0.1544)=2250+2250\times0.1544$
$2250\times0.1544 = 347.4$
So $2250 + 347.4=2597.4$ (more accurately, using the calculator value of $(1.024)^6$:
$2250\times1.15438 = 2250\times1.15438 = 2250\times1.15438\approx2597.355$

Answer:

The total amount Gavin will have in his account at the end of 6 years is approximately $\$2597.36$ (or $\$2597.35$ depending on the calculator precision). If we round to the nearest dollar, it's $\$2597$.