Henry begins a savings account with 500 dollars The savings account accumulates 2 point 5 percent annual interest based on the equation cap v sub h is equal to 500 times 1 point 0 2 5 to the t th power , where cap v sub h is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
Answer
A
cap v sub cap A is equal to 500 times 1 point 0 2 5 raised to the t minus 3 power and cap v sub cap A is equal to 538 point 4 5 times 1 point 0 2 5 to the t th power
B
cap v sub cap A is equal to 500 times 1 point 0 2 5 raised to the t minus 3 power and cap v sub cap A is equal to 464 point 3 0 times 1 point 0 2 5 to the t th power
C
cap v sub cap A is equal to 500 times 1 point 0 2 5 raised to the t plus 3 power and cap v sub cap A is equal to 464 point 3 0 times 1 point 0 2 5 to the t th power
D
cap v sub cap A is equal to 500 times 1 point 0 2 5 raised to the t plus 3 power and cap v sub cap A is equal to 538 point 4 5 times 1 point 0 2 5 to the t th power
Explanation
Because Andres starts 3 years after Henry, his account earns interest for t − 3 years, so its value is 500 × 1.025^(t − 3). Rewriting this as a multiple of 1.025^t gives (500 ÷ 1.025^3) × 1.025^t, which is approximately 464.30 × 1.025^t. Thus the equations with t − 3 and 464.30 are correct.
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