Question

27. The interest rate that doubles a sum in 10 years is

a) 12%
b) 11%
c) 10%
d) 9%​

Answer 1

Interest rate of 7%.

Explanation:

The compound interest formula is given by:

`A(t) = P(1 + (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 + (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%.