Question

An investment will pay you $23,000 in 9 years. The appropriate discount rate is 9 percent compounded daily.

Required:

What is the present value?

Answer 1

Assuming 9% is nominal rate of interest

interest rate = r = 9%

Period = t = 9 years

Number of compounding periods = n = 365 days

Future value = $23,000

Assuming 365 days a year

Present value = Future value / [1 + (r / n)]^{n * t}

Present value = $23,000 / [1 + (0.09 / 365)]^{365 * 9}

Apply 'Log' on both sides

Log (present value) = Log [$23,000 / (1.000247)³²⁸⁵]

Log (a / b) = Log a - Log b

Log (present value) = Log ($23,000) - Log (1.000247)³²⁸⁵

Log (present value) = 4.361728 - (3285 * 0.000107)

Log (present value) = 4.009993

Apply 'Antilog' on both sides

Antilog [Log (present value)] = Antilog (4.009993)

Present value = $10,232.76

Present value = $10,232.76