Question

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

Explanation:

Step1: Identify formula and values

The compound interest formula is \( A = P(1 + r)^t \), where \( P = 6000 \), \( r = 0.05 \), \( t = 2.5 \).

Step2: Calculate for t=2 (first 2 years)

For \( t = 2 \), \( A_2 = 6000(1 + 0.05)^2 = 6000(1.05)^2 = 6000 \times 1.1025 = 6615 \).

Step3: Calculate interest for 0.5 year

After 2 years, principal is \( 6615 \). Interest for 0.5 year: \( I = 6615 \times 0.05 \times 0.5 = 165.375 \).

Step4: Total amount after 2.5 years

\( A = 6615 + 165.375 = 6780.375 \), closest to $6,778.

Answer:

$6,778