Final answer:
To calculate how long it will take for a bank account with an initial deposit of $500 to reach $600 at a 5% simple interest rate, you first determine the total interest required ($100), then use the formula I = Prt to solve for time. The calculation shows that it will take 4 years for the account to reach $600.
Step-by-step explanation:
To determine how long it will take for an account to reach $600 with an initial deposit of $500 at a simple interest rate of 5%, we can use the simple interest formula I = Prt, where I is the interest, P is the principal amount, r is the rate, and t is the time in years.
First, we calculate the total interest needed for the account to reach $600:
- Total amount desired = $600
- Principal (initial amount) = $500
- Interest needed = Total amount - Principal
- Interest needed = $600 - $500 = $100
Next, we use the formula I = Prt to solve for time (t):
- I = $100
- P = $500
- r = 0.05 (5% expressed as a decimal)
- $100 = $500 × 0.05 × t
- $100 = $25t
- t = $100 / $25
- t = 4 years
Therefore, it will take 4 years for the account to reach $600.