suppose that $400 is placed in an account that pays 14% interest compounded each year. assume that no…
suppose that $400 is placed in an account that pays 14% 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 formula for compound interest 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=$400$, $r = 0.14$, and for part (a), $t = 1$.
Step2: Calculate amount after 1 year
Substitute the values into the formula: $A_1=400\times(1 + 0.14)^1=400\times1.14 = 456$.
Step3: Calculate amount after 2 years
For part (b), $t = 2$. Substitute $P = 400$, $r=0.14$, and $t = 2$ into the formula $A = P(1 + r)^t$. So $A_2=400\times(1 + 0.14)^2=400\times1.14^2=400\times1.2996 = 519.84$.
Answer:
(a) $456 (b) $519.84