Question

27. The interest rate that doubles a sum in 10 years is
a) 12%
b) 11%
c) 10%
d) 9%​

Answer 1

Answer:

Interest rate of 7%.

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

In this question:

We want to find t for which $A(t) = 2P$ when $n = 1, t = 10$. So

$A(t) = P(1 + \frac{r}{n})^{nt}$

$2P = P(1 + r)^{10}$

$(1 + r)^10 = 2$

$\sqrt[10]{(1 + r)^10} = \sqrt[10]{2}$

$1 + r = 1.07$

$r = 0.07$

So a interest rate of 7%.