Question

The graph shows the discounted value of $1 over time. Move the slider to change the compound interest rate and observe how the curve for the present value of $1 changes. The red dotted cursor lines show the present value of $1 at a specific time period in the future. Drag on the graph to select different time periods.

PV​N​​=​FV​N​​​​1​​=​(1+I)​N​​​​1​​=​(1+0.050)​3.0​​​​1​​=​1.16​​1​​=$0.86

What is the present value of $1 due in 3 years when the discount interest rate is 10%?

1. $1.33
2. $1.00
3. $0.75
4. $0.10

-Select-abcdItem 1

2. How much is each $1 due in 14 years at a discount rate of 5% worth today?

1. $0.86
2. $0.51
3. $1.98
4. $1.00

-Select-abcdItem 2

3. Bond Long will pay $1 in 20 years with a discount interest rate of 5% and Bond Short will pay $1 in 5 years with a discount interest rate of 10%. Which bond has the higher present value?

1. Long greater than Short
2. Short greater than Long
3. Long and Short have same present value
4. Not enough information to determine

Answer 1

Answer 1)

Future value = $1.00

Time period = 3 years

Discount rate = 10%

Present value = Future value / (1 + Discount rate)^{Time period}

= $1.00 / (1 + 0.10)³

= $0.75 (Option C)

Answer 2)

Future value = $1.00

Time period = 14 years

Discount rate = 5%

Present value = Future value / (1 + Discount rate)^{Time period}

= $1.00 / (1 + 0.05)¹⁴

= $0.51 (Option B)

Answer 3)

Present value of Bond Long = $1.00 / (1 + 0.05)²⁰ = $0.38

Present value of Bond Short = $1.00 / (1 + 0.10)⁵ = $0.62

Present value of "Bond Short" is more than the present value of "Bond Long". Thus, the correct answer is option B