Assume here that 10 percent is a reasonable annual rate. Present value is then determined which is equal to the payment amount with all interest removed. The formula to determine the present value of $1 at a designated point in the future is $1 divided by (1 + i) raised to the nthpower with “n” being the number of periods and “i” the appropriate interest rate. In this case, because payment is due in five years, the present value $1 is $1/(1.10)5, or 0.62092. This factor can then be multiplied by the actual cash payment to determine its present value.
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Although cash is conveyed over an extended period of time in this purchase, a reasonable rate of interest is not being explicitly paid. Thus, once again, a present value computation is necessary to pull out an appropriate amount of interest and leave just the cost of the asset. The present value of the payments (the principal) is the cash paid after all future interest is mathematically removed. That process has not changed. Here, cash is not conveyed as a single amount but rather as an annuity—an equal amount paid at equal time intervals. An annuity can be either an ordinary annuity with payments made at the end of each period or an annuity due with payments starting immediately at the beginning of each period. The specific series of payments in this question creates an annuity due pattern because the first $10,000 is conveyed when the contract is signed. As before, a mathematical formula can be constructed to determine the applicable present value factor. [6] Tables, a calculator, or a computer spreadsheet can also be used. If a reasonable rate is assumed to be 12 percent per year, the present value of a $1 per year annuity due of five periods with a rate of 12 percent is 4.0374. [7]
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