Question

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

Answer 1

Answer:

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