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

Explanation:

Step1: Identify values

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

Step2: Split time for compounding

For the first 2 years, use the compound - interest formula for whole years. For the remaining half - year, use simple interest on the amount after 2 years. For 2 years: $A_1=P(1 + r)^2=6000\times(1 + 0.05)^2=6000\times1.05^2=6000\times1.1025 = 6615$

Step3: Calculate simple interest for half - year

The simple interest formula for half - year ($t=\frac{1}{2}$) on $A_1$ is $I=A_1\times r\times t$. Here, $I = 6615\times0.05\times\frac{1}{2}=6615\times0.025 = 165.375$

Step4: Find final amount

$A=A_1+I=6615 + 165.375=6780.375\approx6778$

Answer:

$6,778$