Question 48

The least number of complete years in which a sum of money will be more than doubled at 10% compound interest is ________.

Solution

Since the number is more than double, the total amount will be at least twice the number.

If the number is x, the amount will be more than 2x.

Thus, $$2x\ge\ x\left(1+\frac{1}{10}\right)^{^r}$$

$$\left(1+\frac{1}{10}\right)^{^{r\ }}\ge\ 2$$

For r = 8, the value of $$\left(1.1\right)^r=2.143$$

Thus, the value of r will be 8.

Thus, the correct option is B.

Alternative:

No. of years in which a sum of money invested at r% compounded annually amounts to double is 72/r years

So, no. of years in which the amount will be doubled = 72/10 = 7.2 years

So, the least no. of years for which the amount will be more than doubled will be 8 years.


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