Sydney wins a prize. She has a choice of receiving a payment of $160,000 immediately or of receiving a deferred perpetuity with $10,000 annual payments, the first payment occurring in exactly four years. Which has a greater present value if the calculation is based on an annual effective interest rate of 5%? How about if the annual effective rate used is 6%? What real life considerations should enter into Sydney’s choice besides maximizing her present value?

She has a choice of receiving a payment of $160,000 immediately or of receiving deferred perpetuity with $10,000 annual payments, the first payment occurring in exactly four years.

A) i= 5%

First, we need to determine the value of the perpetuity four years from now.

Perpetuity= 10,000/0.05= 200,000

Now, we can calculate the present value:

PV= 200,000/(1.05^4)= $164,540.50

B) i= 6%

Perpetuity= 10,000/0.06= $166,666.67

PV= $166,666.67/1.06^4= $132,015.61

C) She should consider her necessities of cash and the value of the products she can purchase now.

Parrain Parrain · Answer 2 · 2022-04-01T16:06:24+02:00

Based on the present values of the immediate payment and the perpetuity, the greater present value at 5% is the Perpetuity.

At a rate of 6%, the greater present value would be the immediate payment.

Some considerations that Sydney should take into account include:

Her age and how long she can keep receiving the perpetuity.
Current investment opportunities that could yield higher rates than the perpetuity.

What is the present value of the perpetuity?

At 5%, the present value is:

= (Annual payment / Rate) / (1 + Rate) ^ number of years till first payment - 1

= (10,000 / 5%) / ( 1 + 5%)⁴⁻¹

= $172,767.50

At 6%, the present value is:
= (10,000 / 6%) / ( 1 + 6%)⁴⁻¹

= $139,936.50

At 5%, the perpetuity is larger than the immediate payment of $160,000.

At 6% however, the immediate payment is larger.

Find out more on perpetuities at https://brainly.com/question/17157614.