Final answer:
The present value of $1,000 paid at the end of each of the next 100 years with a 7% interest rate is calculated using the present value of an annuity formula. With such a long time frame, the formula simplifies since (1 + r)^-n approaches zero, thus the approximate present value is $14,285.71.
Step-by-step explanation:
To calculate the present value of $1,000 paid at the end of each of the next 100 years with an interest rate of 7% per year, we can use the formula for the present value of an annuity. The present value of an annuity formula is PV = Pmt × [(1 - (1 + r)^-n) / r], where Pmt is the annual payment, r is the interest rate per period, and n is the number of periods.
In this case, the annual payment Pmt is $1,000, the interest rate r is 0.07 (or 7%), and the number of periods n is 100. Plugging these values into the formula, we get PV = $1,000 × [(1 - (1 + 0.07)^-100) / 0.07].
To solve this, we can calculate (1 + 0.07)^-100 using a calculator and then perform the rest of the arithmetic to arrive at the present value. However, due to the nature of the formula, as n becomes very large, the (1 + r)^-n term becomes very close to zero, especially for r greater than zero, which simplifies our calculation.
Therefore, we can approximate the present value by disregarding the (1 + r)^-n term, leading to an approximate PV = Pmt / r = $1,000 / 0.07 = $14,285.71.
This is only an approximate value, and the exact calculation would require precise computation using the formula provided.