Question

suppose that $800 is placed in an account that pays 8% interest compounded each year. assume that no withdrawals are made from the account. follow the instructions below. do not do any rounding. (a) find the amount in the account at the end of 1 year. (b) find the amount in the account at the end of 2 years.

Explanation:

Step1: Recall 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, $P=\$8000$, $r = 0.08$.

Step2: Calculate amount at the end of 1 year

For $t = 1$, substitute $P = 8000$, $r=0.08$ into the formula $A = P(1 + r)^t$. So $A_1=8000\times(1 + 0.08)^1=8000\times1.08 = 8640$.

Step3: Calculate amount at the end of 2 years

For $t = 2$, substitute $P = 8000$, $r = 0.08$ into the formula $A = P(1 + r)^t$. So $A_2=8000\times(1 + 0.08)^2=8000\times1.08^2=8000\times1.1664 = 9331.2$.

Answer:

(a) $8640
(b) $9331.2