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

You could it is a chance of 4/12 or 0.333...

What is the rate on an investment that doubles

markusfloyd9192

10.01.2022

The rate at which the investment gets double is 7.776

Step-by-step 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 × $(1+\dfrac{rate}{4\times 100})^{4\times Time}$

Or, 2 × P = P × ( 1 + $\dfrac{\textrm R}{400})^{\textrm 36}$

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

Or, $2^{\frac{1}{36}}$ = 1 + $\dfrac{\textrm R}{400}$

or, 1.01944 - 1 = $\dfrac{\textrm R}{400}$

or, 0.01944 = $\dfrac{\textrm R}{400}$

∴ R = 0.01944 × 400 = 7.776

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

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