Final answer:
To find how long it will take for Larry to have $500 in the account, we can use the continuous compound interest formula. Plugging in the given values, we find that it will take Larry approximately 11.16 years to have $500 in the account.
Step-by-step explanation:
To find how long it will take for Larry to have $500 in the account, we can use the continuous compound interest formula:
A = P * e^(rt)
Where A is the amount of money in the account, P is the initial deposit, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
Plugging in the given values, we have:
$500 = $350 * e^(0.028t)
Dividing both sides by $350, we get:
e^(0.028t) = 500/350
Simplifying further:
e^(0.028t) = 1.4286
Taking the natural logarithm of both sides:
0.028t = ln(1.4286)
Dividing both sides by 0.028, we get:
t = ln(1.4286)/0.028
Using a calculator, we can find that t is approximately 11.16 years. Therefore, it will take Larry approximately 11.16 years to have $500 in the account.