Question

8.6.50 How long will it take for an investment to triple, if interest is compounded continuously at 7%? It will take years before the investment triples. (Round to the nearest tenth of a year.)

Answer 1

The time required for Investment to triple:

Let us assume that $1 is the present value of the investment and we need to determine time period for it to become $3.

We can use the following formula:

FV = PV X e^rt

where FV = Future Value

PV = Present Value

e = 2.7183 (Constant)

r = Rate of Interest

t = Number of Periods

Let's Place values in formula,

FV = PV X e^rt

3 = 1 X e^{0.07 x t}

3 = e^{0.07 x t}

In(3) = 0.07 X t

t = In(3) / 0.07

t = 1.09861228867 / 0.07 (Placing Value of Natural log of 3)

t = 15.6944612667

After rounding

t = 15.7 Years.

Answer: It will take 15.7 years before the investment triples.