How long wiil it take a given sum of money (Say. in Rupees) to increase 4 times its present value when?

Question

compounded half yearly at 7% rate of interest?

Answer 1

The formula for determining compound interest is:
At = Ao (1 + r/n)^(n*t)

To determine how long it takes your money to double, use the following:
At = 2 = amount at time t
Ao = 1 = amount at beginning
r = .07 (7%) = rate of interest
n = 2 = number of times compounded yearly

At = Ao (1 + r/n)^(n*t)
2 = 1 * (1 + .07/2)^(2t)
2 = 1.035^2t
log 2 = 2t log 1.035
log 2 / log 1.035 = 2t
t = (0.30103 / 0.01494) / 2 = 10.07 years (solution)

Check:
At = Ao (1 + r/n)^(n*t)
2 = 1 * (1 + .07/2)^(2*10.07)
2 = 1.035^20.14
2 = 1.9994 (close enough!)

Now, for the above formula, to find t, given the other values:
At = Ao (1 + r/n)^(n*t)
At / Ao = (1 + r/n)^(n*t)
log (At / Ao) = (n*t) log (1 + r/n)
n * t = log (At/Ao) / log (1 + r/n)
t = log (At/Ao) / n log (1 + r/n)