Question

suppose that $200 is loaned at a rate of 10%, compounded annually. assuming that no payments are made, find the amount owed after 8 years. do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years.
Here, $P=\$200$, $r = 0.1$ (since $10\%=0.1$), and $t = 8$.

Step2: Substitute the values into the formula

$A=200\times(1 + 0.1)^8$.
First, calculate $(1 + 0.1)^8$.
$(1 + 0.1)^8=1.1^8$.
$1.1^8=2.14358881$.
Then, multiply by the principal amount: $A = 200\times2.14358881$.
$A = 428.717762$.

Step3: Round the answer

Rounding to the nearest cent, $A\approx\$428.72$.

Answer:

$428.72$