Question

The amount of time it takes for an investment to double in value is called the doubling time for the investment. If the doubling time for a $10,000 investment is seven years and the interest on the investment is compounded annually, what must be the annual rate of interest?

Answer 1

Answer:

Compounding interest rate, r = 10.41%

Explanation:

As the investment will be doubled after 7 years from now, the future value of the current investment will be = $10,000 × 2 = $20,000

Therefore,

Number of periods (years), n = 7

Future value, FV = $20,000

Principal = Present Value, PV = $10,000

we have to determine the compounding interest rate, r.

We know,

r = $[(\frac{FV}{PV})^{\frac{1}{n}} - 1]$

Putting the values into the formula, we can get,

r = $[(\frac{20,000}{10,000})^{\frac{1}{7}} - 1]$

or, r =$(2^{\frac{1}{7}} - 1)$

With the help of calculator, we can find the value of $2^{\frac{1}{7}}$ = 1.1041

or, r = (1.1041 - 1)

or, r = 0.1041

Therefore, interest rate = 10.41%