Question

At what nominal annual rate of interest will money double itself in seven ​years, one month if compounded monthly​? Question content area bottom Part 1 The nominal annual rate of interest for money to double itself in seven ​years, one month is enter your response here​% per annum compounded monthly. ​(Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

The nominal annual rate of interest to double money in seven years and one month with monthly compounding would be calculated using the compound interest formula, with A = 2P, n = 12 and t = 7 + 1/12 years. The exact rate requires solving for r in the equation 2 = (1 + r/12)^(12*(7 + 1/12)).

Step-by-step explanation:

To calculate the nominal annual rate of interest needed for money to double in seven years and one month with monthly compounding, one can use the compound interest formula:

A = P(1 + r/n)nt

Where:

• A is the amount after time t,
• P is the principal amount (initial investment),
• r is the annual nominal interest rate (in decimal form),
• n is the number of times interest is compounded per year,
• t is the time the money is invested for in years.

To double the investment, A = 2P.

Here, n = 12 (monthly compounding) and t = 7 years + 1 month which is 7 + 1/12 years.

Setting up the equation 2 = (1 + r/12)12*(7 + 1/12), and solving for r gives us the nominal annual interest rate required. This calculation requires iterative methods or a financial calculator since it is not straightforward algebra.

Once r is found, it is expressed in percentage form to answer the question. Remember to round the final rate to four decimal places.