Question

1. If the interest rate were 6%, which of these investments would you prefer?       Show your calculations!

1. A single payment of $500 in year 3
2. A payment of $40 a year for 20 years starting in one year’s time
3. A perpetuity of $30 a year starting in one year’s time
4. A perpetuity of $50 a year starting in one year’s time

2. Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3? Show your calculations!

1. $2,200.00
2. $2,238.47
3. $2,309.16
4. $2,468.69    

3. Mr. Bean wants to begin saving for his daughter’s college education and you estimate that he         will need $150,000 in 17 years. If you feel confident that he can earn a compound interest of         8%, how much does he need to invest today? Show your calculations!

1. $40,540.34
2. $8,823.53
3. $150,000
4. $8,169.93

Answer 1

Requirement 1:

Let’s compute PV of each option and compare:

A)

PV = FV/(1+r) ⁿ

     = $ 500/ (1+0.06)³ = $ 500/ (1.06)³

     = $ 500/1.191016 = $ 419.81

B)

PV = C x [1 - (1+r)^-n/r]

    = $ 40 x [1 - (1+0.06)^-20/0.06]

  = $ 40 x [1 - (1.06)^-20/0.06]

    = $ 40 x [(1 - 0.311804726886084)/0.06]

     = $ 40 x (0.688195273113916/0.06)

     = $ 40 x 11.4699212185653

= $ 458.80

C)

PV = C /r = $ 30/0.06 = $ 500

D)

PV = C /r = $ 50/0.06 = $ 833.33

Option “D. Perpetuity of $ 50” is preferable as it has highest present value.

Requirement 2:

FV = C₁ x (1+r)² + C₂/(1+r)¹ + C₃/(1+r)⁰

    = $ 600 x (1+0.034)² + $ 800 x (1+0.034)¹ + $ 1,000 x (1+0.034)⁰

    = $ 600 x (1.034)² + $ 800 x (1.034) + $ 1,000

    = $ 600 x 1.069156 + $ 800 x 1.034 + $ 1,000

   = $ 641.4936 + $ 827.20 + $ 1,000

= $ 2,468.6936 or $ 2,468.69

Accumulated value at the end of year 3 is $ 2,468.69

Option “D. $ 2,468.69” is correct answer.

Requirement 3:

PV = FV/(1+r) ⁿ

     = $ 150,000/ (1+0.08)¹⁷ = $ 150,000/ (1.08)¹⁷   

   = $ 150,000 / 3.70001805480086

= $ 40,540.3427168068 or $ 40,540.34

Mr. Bean need to save $ 40,540.34 today.

Option “A. $ 40,540.34” is correct answer.