Final answer:
To find the number of years it took for $750 to grow to $1405 at a 7% interest rate compounded monthly, we can use the formula for compound interest.
Step-by-step explanation:
To find the number of years it took for $750 to grow to $1405 at a 7% interest rate compounded monthly, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the initial amount is $750, the final amount is $1405, the interest rate is 7%, and the interest is compounded monthly (n = 12). We need to solve for t.
Plugging in the values, we have: $1405 = $750(1 + 0.07/12)^(12t)
Now, we can isolate t by dividing both sides of the equation by $750 and taking the natural logarithm of both sides:
ln($1405/$750) = ln((1 + 0.07/12)^(12t))
Finally, we can solve for t by dividing both sides by ln((1 + 0.07/12)) and simplifying the equation:
ln($1405/$750) / ln((1 + 0.07/12)) = 12t
t = [ln($1405/$750) / ln((1 + 0.07/12))] / 12
Using a calculator, we can find that t is approximately 4.85 years. Therefore, the money was in the bank for about 4.85 years.