To determine the annual rate of interest compounded annually that will double an investment in 7 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case, we are given that the investment doubles in 7 years. This means that the final amount (A) is twice the initial investment (P). Therefore, we can rewrite the formula as:

2P = P(1 + r/n)^(nt)



To solve for the annual interest rate (r), we can divide both sides of the equation by P and simplify:

2 = (1 + r/n)^(nt)

Taking the logarithm of both sides will help us isolate the exponent:

log(2) = log((1 + r/n)^(nt))

Using the property of logarithms, we can bring down the exponent:

log(2) = nt * log(1 + r/n)

Now, we can solve for r by isolating it:

log(2) / nt = log(1 + r/n)

Next, we can eliminate the logarithms by exponentiating both sides:

2^(1/nt) = 1 + r/n

Simplifying further:

2^(1/nt) - 1 = r/n

To find the annual interest rate (r), we need to multiply both sides by n:

r = n * (2^(1/nt) - 1)

In this case, we are compounding annually, so n = 1. Plugging in n = 1:

r = 1 * (2^(1/7) - 1)

Using a calculator, we can evaluate this expression to find the annual interest rate:

r ≈ 0.104090 or 10.4090%

Therefore, an annual interest rate of approximately 10.4090% compounded annually will double an investment in 7 years.

As Per Rule No R=72/N
R = 72/7

Ans Is 10.41%