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

mario 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? $6,118 $6,075 $6,778 $6,456

mario 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? $6,118 $6,075 $6,778 $6,456

Answer

Explanation:

Step1: Identify the values of P, r and t

$P = 6000$, $r=0.05$, $t = 2.5$

Step2: Substitute values into the formula

$A=P(1 + r)^{t}=6000\times(1 + 0.05)^{2.5}$ First, calculate $(1 + 0.05)^{2.5}$. Let $x=(1 + 0.05)^{2.5}=1.05^{2.5}$. We know that $a^{b}=e^{b\ln(a)}$, so $1.05^{2.5}=e^{2.5\ln(1.05)}$. $\ln(1.05)\approx0.04879$, then $2.5\times\ln(1.05)=2.5\times0.04879 = 0.121975$. $e^{0.121975}\approx1.1309$. $A = 6000\times1.1309=6785.4\approx6778$

Answer:

$6,778$