Question

a sum of money is invested at a rate of 40% per annum. find the minimum number of years after which it will become double if the interest is compounded annually.

Answer 1

Answer:

Step-by-step explanation:

Let's call the initial sum of money "P". After "n" years, the investment will be worth 2P if:

2P = P * (1 + 0.40)^n

Dividing both sides by P:

2 = (1 + 0.40)^n

Taking the natural logarithm of both sides:

ln(2) = n * ln(1 + 0.40)

Dividing both sides by ln(1 + 0.40):

n = ln(2) / ln(1 + 0.40)

Approximating with log base e, the minimum number of years is:

n = ln(2) / ln(1.40) = 5.05 years.

So, the minimum number of years to double the investment is approximately 5.05 years.