It is known that a capital `C_(0)` applied to fixed interest capitalized continuously grows at a rate proportional to the capital present at any instant. If the initial capital has doubled in 5 years, when he will triple? As quadruple?
Formula for capital `C` at time `t` with fixed interest capitalized continuously that grows at rate proportional to the capital present at time `t` is
`C(t)= C_0 e^(rt)` (1)
where `C_0` is initial capital and `r` is interest rate.
You can prove formula (1) by solving differential equation
Let's now solve your problem. Since initial capital is doubled after 5 years we have
We can now calculate `r.`
Now we take natural logarithm.
Now that we have `r` we can calculate anything we want.
When will our initial capital triple?
`C_0 e^(ln2/5 t)=3C_0`
Initial capital will quadruple in 7.92 years.
When will our initial capital quadruple?
Since our capital is doubled every 5 years initial capital should quadruple in 10 years. Let's check that.
Initial capital will quadruple in 10 years.