Final answer:
To determine when the balance of the account will be $1500, we can write an exponential equation using the compound interest formula. After solving the equation, we find that it will take approximately 4.11 years for the balance to reach $1500.
Step-by-step explanation:
To determine when the balance of the account will be $1500, we can write an exponential equation using the compound interest formula:
A = P(1 + r/n)^(nt)
- A is the total amount of money in the account
- P is the principal amount (initial deposit)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
Let's substitute in the given values: P = $1000, r = 0.05, n = 1, and A = $1500. The equation becomes:
$1500 = $1000(1 + 0.05/1)^(1*t)
Simplifying further, we get:
1.5 = 1.05^t
To solve for t, we take the logarithm of both sides:
log(1.5) = t * log(1.05)
Using a calculator, we find that t is approximately 4.11 years.