Question

a client can choose between receiving 10 annual $100,000 retirement payments, starting one year from today, or receiving a lump sum today. knowing that he can invest at a rate of 5 percent annually, he has decided to take the lump sum. what lump sum today will be equivalent to the future annual payments?

Answer 1

To calculate the equivalent lump sum today, we can use the formula for present value of an annuity. The formula is PV = PMT x (1 - (1 + r)^-n) / r. In this case, the payment per period is $100,000, the interest rate is 5% per year, and the number of periods is 10. Therefore, the equivalent lump sum today would be $1,257,789.27.

Step-by-step explanation:

To calculate the equivalent lump sum today, we can use the formula for present value of an annuity. The formula is:

PV = PMT x (1 - (1 + r)^-n) / r

PV = Present Value

PMT = Payment per period

r = Interest rate per period

n = Number of periods

In this case, the payment per period is $100,000, the interest rate is 5% per year, and the number of periods is 10.
Plugging in these values:

PV = $100,000 x (1 - (1 + 0.05)^-10) / 0.05

PV = $100,000 x (1 - 1.628894627535516) / 0.05

PV = $100,000 x (-0.628894627535516) / 0.05

PV = $1,257,789.27

Therefore, the equivalent lump sum today would be $1,257,789.27.