Question

Suppose that you plan to have the following investments:

$1,000 annually on your 23rd through 30th birthdays -- a total of eight investments. Also, suppose that the interest rate for the year between your 23rd and 24th birthdays is expected to be 4.0% per annum and that this rate will increase by 0.25% each year thereafter until your 31st birthday.

a. How much would you have on your 31st birthday?

b. What single rate, compounded annually, from your 23rd through 31st birthdays would get you to the same position as in part a?

Your other investment pays $60,000 every third year (tri-annually) in perpetuity. Your required rate of return is 12.68 percent, compounded daily (365 days in a year).

a. What is the value of this investment today, if the 1st payment occurs 1 year from today?

b. If the 1st payment occurred 4 years from today rather than 1 year from today, what would you pay for this investment today?

Answer 1

a. How much would you have on your 31st birthday?
ANSWER

You would have a total of $8,856.24 on your 31st birthday.

 

WORKING

$1,000 at 4% for 8 years compounded annually

$1,000 × 1.04^8 = $1,000 × 1.32 = $1,320

$1,000 at 4.25% for 7 years compounded annually$1,000 × 1.0425^7 = $1,000 × 1.29 = $1,290

$1,000 at 4.5% for 6 years compounded annually$1,000 × 1.045^6 = $1,000 × 1.26 = $1,260

$1,000 at 4.75% for 5 years compounded annually$1,000 × 1.0475^5 = $1,000 × 1.23 = $1,230

$1,000 at 5.0% for 4 years compounded annually$1,000 × 1.05^4 = $1,000 × 1.20 = $1,200

$1,000 at 5.25% for 3 years compounded annually$1,000 × 1.0525^3 = $1,000 × 1.17 = $1,170

$1,000 at 5.5% for 2 years compounded annually$1,000 × 1.055^2 = $1,000 × 1.14 = $1,140

$1,000 at 5.75% for 1 year compounded annually$1,000 × 1.0575^1 = $1,000 × 1.11 = $1,110

Total = $8,856.24

 

b. What single rate, compounded annually, from your 23rd through 31st birthdays would get you to the same position as in part a?

ANSWER

The equivalent single rate, compounded annually, would be 5.375%.

 

WORKING

$1,000 × 1.05375^8 = $1,000 × 1.32 = $8,856.24

 

a. What is the value of this investment today, if the 1st payment occurs 1 year from today?

ANSWER

The value of this investment today is $173,830.48.

 

WORKING

$60,000 × 1.1268^3 = $60,000 × 1.38 = $173,830.48

 

b. What is the value of this investment today, if the 1st payment occurs 3 years from today?

ANSWER

The value of this investment today is $126,294.16.

 

WORKING

$60,000 × 1.1268^1 = $60,000 × 1.12 = $126,294.16

 

b. If the 1st payment occurred 4 years from today rather than 1 year from today, what would you pay 

for this investment today?

ANSWER

$1,000 × 1.05375^4 = $1,000 × 1.23 = $11,294.16