Question

How long does it take a present value amount to triple if the expected return is 10.2%? Answer to 2 decimal points.

Answer 1

Assumption: Returns are annual

Suppose I have $ x (PV) that I invest today.

We have to calculate how much time it will take to make it $ 3x (FV) with 10.2% returns.

FV - Future value of returns

PV - Present value of returns

n - frequency at which interest is charged

t - time period

for annual returns, n=1 (frequency of interest rate charge), r = 10.2/100 = 0.102

replacing the values, we get

3x = x ( 1 + (0.102/1))^t

3 = (1.102)^t

Taking log both the sides, we have

ln(3) = ln (1.102 ^ t)

From logarithmic function, we get-

ln(3) = t * ln(1.102)

Calculating the values of log-

1.099 = t*0.097

t = 11..3

Thus, the present value amount is expected to triple after approximately 11.3 years.