Question

What is the rate on an investment that doubles $5051 in 9 years? Assume interest is compounded quarterly.

Answer 1

The rate at which the investment gets double is 7.776

Explanation:

Given as :

The principal investment = $ 5051

The time period of investment = 9 years

Let The rate of interest = R % compounded quarterly

The Amount gets double

So, From Compounded method

Amount = Principal ×
`(1+(rate)/(4* 100))^(4* Time)`

Or, 2 × P = P × ( 1 +
`(\textrm R)/(400))^(\textrm 36)`

Or, 2 = ( 1 +
`(\textrm R)/(400))^(\textrm 36)`

Or,
`2^{(1)/(36)}` = 1 +
`(\textrm R)/(400)`

or, 1.01944 - 1 =
`(\textrm R)/(400)`

or, 0.01944 =
`(\textrm R)/(400)`

∴ R = 0.01944 × 400 = 7.776

Hence The rate at which the investment gets double is 7.776 Answer