Question

What is the value today of a money machine that will pay $4,097.00 every six months for 18.00 years? Assume the first payment is made six months from today and the interest rate is 5.00%.

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Answer format: Currency: Round to: 2 decimal places.

Answer 1

• These cash flows are in the form of annuities.

• Annuity = $4,097

• Number of years = 18 years

• Interest rate = 5% per annum

• Present value of annuity = Annuity × Present Value Annuity Factor (PVAF)

• Present value of annuity = $4,097 × 23.556251 = $96,509.96

• Value today of a money machine is the present value of cash flows from it which is $96,509.96

PVAF

• r = interest rate per period = 5% ÷ 2 = 2.5%
• n = number of periods = 18 years × 2 = 36 periods