suppose that $5500 is placed in an account that pays 2% interest compounded each year. assume that no…
suppose that $5500 is placed in an account that pays 2% 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. $
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula for annual compounding 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=$5500$, $r = 0.02$.
Step2: Calculate amount after 1 year
For $t = 1$, substitute values into the formula: $A_1=5500\times(1 + 0.02)^1=5500\times1.02 = 5610$.
Step3: Calculate amount after 2 years
For $t = 2$, substitute values into the formula: $A_2=5500\times(1 + 0.02)^2=5500\times(1.02)^2=5500\times1.0404 = 5722.2$.
Answer:
(a) $5610 (b) $5722.2