Question

How long does it take for a deposit of $800 to double at 10% compounded continuously?

How many years does it take to double? years
...
days

Answer 1

6.93 years

Explanation:

To determine the time it takes for a deposit to double at a given rate with continuous compounding, you can use the formula:

t = In(2) / (r * In(1 + (p / r)))

where:

t = time (in years)

p = initial deposit

r = annual interest rate (as a decimal)

In this case, p = $800 and r = 0.1 (since the interest rate is 10% per year). Plugging in these values, we get:

t = In(2) / (0.1 * In(1 + (800 / 0.1)))

Simplifying this expression, we get:

t = In(2) / (0.1 * In(1 + 8000))

t = 6.93 years

Therefore, it will take approximately 6.93 years for the deposit to double at 10% compounded continuously.