mano invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula $a =…

mano invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula $a = p(1 + r)^t$, what is the approximate value of the account after 2.5 years?\n$6,075\n$6,118\n$6,456\n$6,778

mano invested $6,000 in an account that pays 5% annual interest compounded annually. using the formula $a = p(1 + r)^t$, what is the approximate value of the account after 2.5 years?\n$6,075\n$6,118\n$6,456\n$6,778

Answer

Explanation:

Step1: Identify values for formula

$P = 6000$, $r=0.05$, $n = 1$, $t = 2.5$. The compound - interest formula is $A=P(1 + \frac{r}{n})^{nt}$.

Step2: Substitute values into formula

$A = 6000(1+\frac{0.05}{1})^{1\times2.5}=6000(1 + 0.05)^{2.5}$.

Step3: Calculate $(1 + 0.05)^{2.5}$

Let $x=(1 + 0.05)^{2.5}=1.05^{2.5}$. Using a calculator, $1.05^{2.5}\approx1.12649$.

Step4: Calculate $A$

$A = 6000\times1.12649\approx6758.94\approx6778$.

Answer:

D. $6,778$