Question

An investment has grown from $50,000 to $100,000 (which means it doubles) in 5 years compounding quarterly.

What was the interest rate? Round to the nearest tenth of a percent.

Answer 1

We can use the formula for compound interest to find the interest rate:

A = P*(1 + r/n)^(n*t)

where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.

In this case, P = $50,000, A = $100,000, n = 4 (since compounding is quarterly), and t = 5. We want to solve for r.

First, we can find the factor by which the initial amount is multiplied after each compounding period:

(1 + r/n)

Since the investment doubles in value, this factor is 2. Therefore,

2 = (1 + r/4)^(4*5)

Simplifying this equation, we get:

2 = (1 + r/4)^20

Taking the 20th root of both sides, we get:

1 + r/4 = 2^(1/20)

Subtracting 1 from both sides and multiplying by 4, we get:

r = 4*(2^(1/20) - 1)

Using a calculator, we get:

r ≈ 6.1%

Therefore, the interest rate is approximately 6.1% per year, compounded quarterly.

Explanation: