Final answer:
To calculate the number of years it takes for an initial deposit to double in an investment account that pays 7% annual interest compounded continuously, we can use the formula for compound interest. By rearranging the formula and solving for the time, we find that it will take about 10 years for the initial deposit to double.
Step-by-step explanation:
To calculate the number of years it takes for an initial deposit to double, we can use the formula for compound interest:
A = P*e^(rt)
Where:
- A is the final amount
- P is the principal amount
- e is Euler's number (approximately 2.71828)
- r is the annual interest rate (0.07 for 7%)
- t is the time in years
Since we want the initial deposit to double, the final amount will be 2 times the principal amount:
2P = P*e^(0.07t)
To solve for t, we can divide both sides by P and take the natural logarithm of both sides:
ln(2) = 0.07t
t = ln(2)/0.07
Calculating this value gives us approximately 9.90 years. So, it will take about 10 years for the initial deposit to double.