Question

(a) For each of the following payment schemes, choose which is better at an interest rate of 5%

i. Receiving $7,000 right now, or $750 per year for 12 years, starting next year.
ii. Receiving $10,000 in 10 years, or receiving $1,000 per year for 5 years, starting now.
(b) For each of the following pairs of options, find the interest rate which would make you indifferent between them.
i. Receiving $1,000 now, or $1,402.55 in five years.
ii. Receiving $166,666.67 now, or $15,000 per year in perpetuity starting next year.

Answer 1

Step-by-step explanation:

(a) i. Payment = $7000

For cash flow payment = $750 (Per year at 5%, for 12 years)

= 750*8.863

= $6697.25

This shows it is better to receive $7000 right now.

ii. FV = $10000

PV = FV(P/F, 5%, 10 years)

= 10000*0.6139

= $6139

And Payment of $1000 per year, for 5 years

PV = 1000 (per year at 5%, for 5 years)

= $1000*7.722

= $7722

It is better to get $1000 per year for 5 years

(b)i. PV = $1000

fV = $1402.55

Interest = i

by formula

1000 = 1402.55 (p/f, i, 5)

1000 =
`(1402.55)/((1 + i)^(5) )`

`\sqrt[5]{(1 + i)^5}` =
`\sqrt[5]{(1402.55)/(1000) }`

1 + i = 1.069

Collect like terms

i = 1.069 - 1

i = 0.069

i ≈ 7%

ii. PV = $166666.67

Perpetuity = 15000

interest is unknown

166666.67 = 15000/i

i = 15000/166666.67

i = 0.089

i ≈ 9%