Question

You inherited $5,000 which you place today in the bank in an account earning 3% interest. How long will it take for the money to double? Show your calculations.

Answer 1

Using the compound interest formula, it will take approximately 23.45 years for $5,000 to double with a 3% interest rate compounded annually

Step-by-step explanation:

To determine how long it will take for an amount of money to double with compound interest, we can use the compound interest formula:

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

Where:

• A = the final amount
• P = the principal amount (initial deposit)
• r = annual interest rate (as a decimal)
• n = number of times interest is compounded per year
• t = number of years

In this case, we want to find t, so we rearrange the formula:

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

Let's plug in the values for this scenario:

• A = 2P (since we want the amount to double)
• P = $5,000
• r = 0.03 (3% interest rate)
• n = 1 (compounded annually)

Now we can calculate:

t = log(2) / (1 * log(1 + 0.03/1))

t ≈ 23.45 years

So, it will take approximately 23.45 years for the $5,000 to double with a 3% interest rate compounded annually.

Answer 2

To determine how long it takes for $5,000 to double at a 3% interest rate, we use the Rule of 72, resulting in a calculation of 72 divided by 3, equating to 24 years.

Step-by-step explanation:

To calculate how long it will take for $5,000 to double at an interest rate of 3%, we can use the Rule of 72. This is a simple way to determine the number of years it will take for an investment to double by dividing 72 by the annual interest rate. In this case, it will be 72 divided by 3. Calculation Steps - Identification of the Rule of 72: 72 / interest rate = doubling time in years .Calculation of doubling time: 72 / 3 = 24 years. Thus, it will take 24 years for your $5,000 to grow to $10,000 at a 3% annual interest rate, compounded annually.