Question

lamar puts $1,500 in a bank account that has a simple interest rate of 4.8%. assuming no other transactions, how long will it take for the account balance to reach $2,600?
enter your answer in years, rounded to two decimal places.
show your work here

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is \( A = P(1 + rt) \), where \( A \) is the final amount, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years.
We know \( P = 1500 \), \( A = 2600 \), \( r = 4.8\% = 0.048 \). We need to solve for \( t \).

Step2: Rearrange the formula to solve for \( t \)

First, divide both sides of the formula by \( P \): \( \frac{A}{P} = 1 + rt \)
Then, subtract 1 from both sides: \( \frac{A}{P} - 1 = rt \)
Finally, divide both sides by \( r \): \( t = \frac{\frac{A}{P} - 1}{r} \)

Step3: Substitute the values into the formula

Substitute \( A = 2600 \), \( P = 1500 \), and \( r = 0.048 \) into the formula:
\( \frac{\frac{2600}{1500} - 1}{0.048} \)
First, calculate \( \frac{2600}{1500} \approx 1.7333 \)
Then, \( 1.7333 - 1 = 0.7333 \)
Now, divide by \( 0.048 \): \( t = \frac{0.7333}{0.048} \approx 15.28 \)

Answer:

15.28