18 mr wilkins deposited $2,500 in a new account at his bank.\n· the bank pays 6.5% interest compounded…
18 mr wilkins deposited $2,500 in a new account at his bank.\n· the bank pays 6.5% interest compounded annually on this account.\n· mr. wilkins makes no additional deposits or withdrawals.\nwhich amount is closest to the balance of the account at the end of 2 years?
Answer
Explanation:
Step1: Identify 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 (in decimal form), and $t$ is the number of years.
Step2: Convert the interest rate to decimal
The annual interest rate $r=6.5% = 0.065$, the principal amount $P = 2500$, and the number of years $t = 2$.
Step3: Substitute values into the formula
$A=2500\times(1 + 0.065)^2=2500\times(1.065)^2$.
Step4: Calculate $(1.065)^2$
$(1.065)^2=1.065\times1.065 = 1.134225$.
Step5: Calculate the final amount
$A=2500\times1.134225=2835.5625\approx2835.56$.
Answer:
$2,835.56$