Question

Present value What is the present value of a security that will pay $20,000 in 20 years if securities of equal risk pay 12% annually? Round your answer to the nearest cent.

Answer 1

1]

present value = future value / (1 + discount rate)^{number of years}

present value = $20,000 / (1 + 12%)²⁰

present value = $2,073.34

2]

a]

present value = future value / (1 + discount rate)^{number of years}

Let us assume the number of years is n.  

$500 = $1,000 / (1 + 3%)ⁿ

1.03ⁿ = ($1,000 / $500)

1.03ⁿ = 2

n = log_1.032

n = 23.45

It will take 23.45 years for $500 to double

b]

present value = future value / (1 + discount rate)^{number of years}

Let us assume the number of years is n.  

$500 = $1,000 / (1 + 9%)ⁿ

1.09ⁿ = ($1,000 / $500)

1.09ⁿ = 2

n = log_1.092

n = 8.04

It will take 8.04 years for $500 to double

c]

present value = future value / (1 + discount rate)^{number of years}

Let us assume the number of years is n.  

$500 = $1,000 / (1 + 21%)ⁿ

1.21ⁿ = ($1,000 / $500)

1.21ⁿ = 2

n = log_1.212

n = 3.64

It will take 3.64 years for $500 to double

d]

present value = future value / (1 + discount rate)^{number of years}

Let us assume the number of years is n.  

$500 = $1,000 / (1 + 100%)ⁿ

2ⁿ = ($1,000 / $500)

2ⁿ = 2

n = log₂2

n = 1

It will take 1 year for $500 to double