question 10\nfind the final amount of money in an account if $2,800 is deposited at 7.5% interest compounded…

question 10\nfind the final amount of money in an account if $2,800 is deposited at 7.5% interest compounded quarterly (every 3 months) and the money is left for 5 years.\nthe final amount is $ \nround answer to 2 decimal places\nquestion help: video i\nsubmit question

question 10\nfind the final amount of money in an account if $2,800 is deposited at 7.5% interest compounded quarterly (every 3 months) and the money is left for 5 years.\nthe final amount is $ \nround answer to 2 decimal places\nquestion help: video i\nsubmit question

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert given values to appropriate form

The principal amount $P=$2800$, the annual interest rate $r = 7.5%=0.075$. Since interest is compounded quarterly, $n = 4$, and the number of years $t = 5$.

Step3: Substitute values into the formula

$A=2800(1 +\frac{0.075}{4})^{4\times5}=2800(1 + 0.01875)^{20}$.

Step4: Calculate the value inside the parentheses

$1+0.01875 = 1.01875$.

Step5: Calculate the exponent part

$(1.01875)^{20}\approx1.449947$.

Step6: Calculate the final amount

$A = 2800\times1.449947\approx4059.85$.

Answer:

$4059.85$