Question

In order that a $10000 investment grow to $20000 in seven years, what μst be the annual rate of interest? Seven years could be called the doubling time for this investment. Notice that it is being assumed that the interest is compounded.

Answer 1

To find the annual rate of interest needed for a $10,000 investment to grow to $20,000 in seven years, we can use the compound interest formula: A = P(1 + r/n)^(nt). Plugging in the given values, we can solve for r to find the annual rate of interest.

Step-by-step explanation:

To find the annual rate of interest needed for a $10,000 investment to grow to $20,000 in seven years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we have A = $20,000, P = $10,000, t = 7, and n = 1 (since it is compounded annually).

Plugging these values into the formula, we get $20,000 = $10,000(1 + r/1)^(1*7). Simplifying the equation, we have 2 = (1 + r)^7. To solve for r, we need to isolate it. Taking the seventh root of both sides, we get (1 + r) = 2^(1/7). Subtracting 1 from both sides, we find r = 2^(1/7) - 1. Using a calculator, we find r ≈ 0.1019, or approximately 10.19%. Therefore, the annual rate of interest needed for the $10,000 investment to double to $20,000 in seven years is approximately 10.19%.