(Monthly compounding) How much would you have to invest today at 12% annual interest, compounded monthly, in order to end up with $1,000 in your investment account at the end of 12 months?

 

I computed the present value of the investment by trial and error. The problem says that, the future value of his investment is equal to 1,000 in order to compute that, I made a series of trial and error to arrive at the correct answer. In the first part of solution which is the long cut method, I show to you the breakdown of interest and future value per month for your own reference. If you saw again problem like this, the word "interest is compounded" it means to say that interest also earns interest. You can observe it on my first computation which is the long cut method that when we are computing for interest through passage of time the interest prior to the current month is being the based amount when we are computing for interest in the current month. Next, the 12% interest rate is stated as per annum so to know what is the interest rate per month, we must divide the interest rate and number of months in a year (12% / 12 months) and the interest rate per month in the problem is 1%. The number of periods in the problem are 12 months because the payment of interest is per month so we need to multiply one year and number of periods the company will pay their interest which is monthly (1 year * 12 months). Just use my templates and formulas in computing problem like this.

Please see the attached file for the complete solution