Present value of a future sum of money is the value today of a dollar to be received in the future. It is the sum of money that must be invested today in order to have the future sum at a specified time in the future, assuming interest will accrue over the time period considered. Simple interest calculates the future value based on the present value and the interest rate.
Compound interest is similar in principle but different in application. In compound interest, the value of a future payment is determined by calculating the present value of the sum of the principal amount plus all interest accruing on the principal from the specified time of receipt until the present time. Interest is then applied to this compound amount for each period until the date of the specified payment.
Basically, the future value of a sum of money (the payment in question) can be determined by using the present value formula, which is FV = PV(1 + i)^n, where FV stands for future value, PV stands for present value, i stands for the interest rate and n stands for the number of periods. This formula can be used to calculate the future value of a sum of money with simple or compound interest, given that you have all the necessary information.
The formula is of particular use in investments, loans, and mortgages. For example, when taking out a loan, a person has to think of how much money will have to be repaid in the future based on the loan taken out. A person can use the present value formula to determine how much the future payment will be. If a loan is taken out for $50,000 compounded annually and the rate of interest is 5%, then the future value of the loan can be determined by taking the present value and multiplying it by 1+(rate of interest) ^ the number of years to maturity, or in this case 1+(.05)^(5). This results in a future value of $67,128.67.
Present value of cumulative future sums is a variation of the present value of a future sum of money and requires accounting for the present values of multiple future payments, rather than just one. The same formula can be used, but the payments must be included in the formula. This means that each future payment must be discounted at the original interest rate, added to the initial present value, and then the calculation is run for the total number of years.
Cumulative present value of future sums is most often used to calculate investments, retirement funds, and mortgages. For example, if a mortgage is taken out on a property, the mortgage will be paid in multiple future payments over a long period of time, usually more than five years. To calculate the present value of the mortgage payments, each future payment must be discounted individually at the original interest rate and then added up to find the cumulative present value of the future payments.
In conclusion, the present value of a future sum of money is used to determine the current value of a payment to be received in the future. It can be used to calculate investments, loans, mortgages, retirement funds and many other things. The formula used to calculate this is FV = PV (1 + i) ^ n, and it is important to have all necessary information as it is integral in calculating the correct future value. Similarly, for calculating the cumulative present value of future sums, the same formula is used, but the payments must be included in the equation and each payment must be discounted individually.
