Final answer:
Find out how many years it takes for $1000 at 6% interest compounded continuously to grow to $2500, we use the continuous compounding formula. With A as $2500, P as $1000, and r as 0.06, we use the natural logarithm to solve for t, which represents time in years.
Step-by-step explanation:
When $1000 is deposited in a savings account at 6% interest compounded continuously, we use the formula for continuous compounding A = Pert,
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- t is the time in years.
For the balance to reach $2500, we set A to $2500, P to $1000, and r to 0.06 (6% written as a decimal).
By rearranging the formula to solve for t, we have:
t = (ln(A/P)) / r
Substituting in the values:
t = ln(2500/1000) / 0.06
This will give us the years required for the balance to reach $2500.