You have an annuity of $500 that begin three years from today and last for a total of fifteen years. Using a discount rate of 7%, calculate the present value of the payments.

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Quizplus · Accepted Answer

The present value of an annuity can be calculated using the formula PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the discount rate per period, and n is the total number of payments. However, since the payments begin three years from today, we must also discount the calculated present value back to today's terms. First, calculate the present value of the annuity as if it started today: PV = $500 * [(1 - (1 + 0.07)^-15) / 0.07] = $500 * 9.107914 = $4,553.957. Then, discount this amount back two years (since it's three years from today but we calculate as if starting today, so we need to adjust for the starting point being in the future): PV = $4,553.957 / (1 + 0.07)^2 = $3,717 (approximately).

You Have an Annuity of $500 That Begin Three Years