Question

Paulo has won the lottery. He is offered a series of payments of $10,000 per year for 10 years. What is the present value of these payments at an interest/discount rate of 6%

Answer 1

The present value of the series of payments is approximately $62,160.16.

Step-by-step explanation:

To calculate the present value of the series of payments, we need to use the present value formula. The formula is:

PV = C * (1 - (1 + r)(-n)) / r

Where PV is the present value, C is the cash flow per period, r is the interest rate per period, and n is the number of periods.

In this case, the cash flow per period (C) is $10,000, the interest rate per period (r) is 6%, and the number of periods (n) is 10. Plugging these values into the formula, we get:

PV = $10,000 * (1 - (1 + 0.06)⁻¹⁰) / 0.06

Solving this equation, the present value of the series of payments is approximately $62,160.16.

Answer 2

PV= $73,600.87

Step-by-step explanation:

Giving the following information:

Annual payments= $10,000

Number of periods= 10 years

Interest rate= 6%

To calculate the present value, we need to use the following formula:

PV= A*{(1/i) - 1/[i*(1 + i)^n]}

A= annual payment

PV= 10,000*{(1/0.06) - 1/[0.06*(1.06^10)]}

PV= $73,600.87