Question

find the compound interest and future value.
principal rate time
$825 3% 9 years
the future value is $ , and the compound interest is $ . do not round intermediate calculations. round your final answers to the nearest cent.

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded annually is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P=\$825$, $r = 0.03$ (since $3\%=0.03$), and $t = 9$.

Step2: Calculate the future value $A$

$A=825\times(1 + 0.03)^9=825\times(1.03)^9$.
$(1.03)^9=1.03\times1.03\times1.03\times1.03\times1.03\times1.03\times1.03\times1.03\times1.03\approx1.304773154$.
$A = 825\times1.304773154\approx1076.447852\approx\$1076.45$.

Step3: Calculate the compound interest $CI$

The compound interest $CI=A - P$.
$CI=1076.45−825=\$251.45$.

Answer:

The future value is $\$1076.45$, and the compound interest is $\$251.45$.