Question

It takes 11.553 years for an initial investment to double at an annual force of interest δ. How long will it take for an initial investment to triple at a nominal rate of interest numerically equal to δ and convertible twice a year?

Answer 1

Answer:

It will take 18.041 years to triple the investment.

Explanation:

$(1+\delta )^{11.553} =2$

We need to solve for delta:

$\delta = \sqrt[11.5530]{2} -1$

delta = 0.06183353

now solve for this rate compounding twice per year to triple the investment:

$(1+0.06183353/2 )^{n*2} =3$

we use logarithmics properties and solve for n:

[tex]2 \times n= \frac{log3}{log(1+06183353/2)

n = 18.04051743

It will take 18.041 years to triple the investment.