10) a compound interest account has accrued an account balance of $1,159.27 over the course of 5 years. the…

10) a compound interest account has accrued an account balance of $1,159.27 over the course of 5 years. the interest rate paid was 3%. which is closest to the principal amount on the account?

10) a compound interest account has accrued an account balance of $1,159.27 over the course of 5 years. the interest rate paid was 3%. which is closest to the principal amount on the account?

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Given $A=$1159.27$, $r = 0.03$, and $t = 5$. We need to solve for $P$. Rearranging the formula for $P$ gives $P=\frac{A}{(1 + r)^t}$.

Step2: Substitute values

Substitute $A = 1159.27$, $r=0.03$, and $t = 5$ into the formula $P=\frac{A}{(1 + r)^t}$. So, $P=\frac{1159.27}{(1 + 0.03)^5}$. First, calculate $(1 + 0.03)^5=(1.03)^5=1.03\times1.03\times1.03\times1.03\times1.03\approx1.159274$. Then, $P=\frac{1159.27}{1.159274}\approx1000$.

Answer:

$1000$