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

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

Answer

Explanation:

Step1: Identify values

Given ( P = 6000 ), ( r = 0.05 ), ( t = 2.5 ).

Step2: Apply compound interest formula

Substitute into ( A = P(1 + r)^t ):
( A = 6000(1 + 0.05)^{2.5} )
First, calculate ( 1.05^{2.5} ). Note that ( 1.05^{2.5}=1.05^{2 + 0.5}=1.05^2\times1.05^{0.5} ).
( 1.05^2 = 1.1025 ), ( 1.05^{0.5}=\sqrt{1.05}\approx1.0247 ).
Multiply: ( 1.1025\times1.0247\approx1.1297 ).
Then, ( A = 6000\times1.1297\approx6778 ).

Answer:

$6,778