The main assumption is that the winner receives the entire sum in one installment and invests it in an account with a compound interest of 9% annually for two years. The alternative to this is receiving the initial $11,000,000 in 26 annual installments. The formula and the calculations that describe the final sum that the lottery winner will receive after 26 years is the following:
A = 11000000(1+0.09/12)(12(26)) The present value of the money that will be received is a notion that contrast the value of the money that an individual has now with the value of it over time. The example of compound interest is an ideal representation of this concept since, through this investment, a person will have a significant increase of the initial investment over a given period. The present value will allow comparing this with the current sum to determine if it is worth investing in. Using the example of the lottery prize, the present value of this money is $423,076, and it will increase by $423,076 over the course of repayment, which is 26 months. If the whole sum of $11,000,000 was invested with an annual interest rate of 9% with monthly compounding interest, the winner would receive $113,200,875.80. The basis of this concept is that the interest-on-interest notion. The interest is added to the investment sum each month. In order to make a clear comparison between the present value of the lottery money and the investment option available, the future value of it must be calculated as well. This is the outcome of the compound interest calculations. Hence the future value is A or $113,200,875. Present value, in this case, was calculated using the following formula: B = 113,200,875(1/1+0.09)26
Hence, the present value of this investment is $12,043,725, which is more than a person would receive if annual installments were chosen as an option. To sum up, monthly compounding of interest means that each month, the interest rate is added to the initial investment. The present value allows comparing the current value of the money with the sum that the individual will receive upon investment.