Question

What rate of interest compounded annually is required to double an investment in 25 years?

Answer 1

The Rate of interest compounded annually is 2.8

Explanation:

Given as :

The Principal o investment = P

The Amount of Investment = 2 × P

The time period of investment = 25 years

Le The rate of interest compounded annually = R

So, From compounded method :

Amount = Principal ×
`(1+(Rate)/(100))^(Time)`

Or, 2 P = P ×
`(1+(Rate)/(100))^(25)`

Or,
`(2P)/(P)` =
`(1+(Rate)/(100))^(25)`

Or, 2 =
`(1+(Rate)/(100))^(25)`

Or,
`2^{(1)/(25)}` = 1 +
`(Rate)/(100)`

Or, 1.028 = 1 +
`(Rate)/(100)`

Or, 1.028 - 1 =
`(Rate)/(100)`

Or, .028 =
`(Rate)/(100)`

So, Rate = 0.028 × 100 = 2.8

Hence The Rate of interest compounded annually is 2.8 Answer