If your company purchases an annuity that will pay 50000year

If your company purchases an annuity that will pay $50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase?

Solution

Annual Payment = $50,000
Period = 10 years
Discount Rate = 11%

Present Value of Annuity = $50,000 + $50,000/1.11 + $50,000/1.11^2 + ... + $50,000/1.11^9
Present Value of Annuity = $50,000 * 1.11 * (1 - (1/1.11)^10) / 0.11
Present Value of Annuity = $50,000 * 6.5370
Present Value of Annuity = $326,850

So, value of annuity on purchase date is $326,850