Question

1. A company wants to purchase a trailer, which only has a useful life of 10 years. The maintenance costs during the first year will be $500 and is expected to increase at a rate of $100 per year, assuming maintenance costs occur at the end of the year. The firm wants to set up a maintenance account that earns 1.5% annual interest to pay for the maintenance cost, how much does the firm need to deposit in the account now? (4 pts)
2. You want to reach a goal of $6000 in five years, you plan on making five payments at the end of each year. If i = 1%, how much do you need to deposit at the end of each year? (3 pts)
3. Kevin found $800 stashed in a book for 30 years. How much money has he lost by not putting it in a bank account at two percent annual compound interest all these years? (3 pts)
4. A small fabricator of plastics needs to purchase an extrusion moulding machine for $150,000. The company will borrow money from a bank at an interest rate of 5% over five years and is to be repaid in equal instalments, what is the instalment? (3 pts)
5. If the same company expects its product sales to be slow during the first year, but to increase subsequently at an annual rate of 6%. The company therefore arranges with the bank to pay off the loan on a “geometric gradient,” which results in the lowest payment at the end of the first year and each subsequent payment being 6% over the previous one. Determine the five annual payments. (5pts)

Answer 1

1) The cost is $500 for the first year and increasing by $100 each year up to the 10th year.

500 + 600 + 700 + ......+ 1300 + 1400 = 9500
Total cost will be $9500
Interest rate is given as 1.5%

9500 / ( 1.015 ^ 10 ) = 8185.84

The firm needs to deposit $8185.84 in that account now.

2) Future value is 6000 while there are 5 payments

=PMT(1%,5,,-6000,0)
= 1176.24

3) We need FV after 30 years and interest rate is 2%

=FV(2%,30,,-800,0)
= 1449.09

OR
800 * ( 1.02 ^ 30 ) = 1449.0893

1449.09 - 800 = 649.09

4) The loan is of $150,000 for 5 year

=PMT(5%,5,-150000,,0)
= 34646.22
$34646.22 will be the yearly installment.

=PMT(5%/12,60,-150000,,0)
= 2830.69

This will be monthly installment

First four questions have been answered.

I am answering the 5th question because it has been requested.

5) It is mentioned that the company will pay the lowest amount at the end of the 1st year and that will rise by 6% each year.
Now that means the increase is uniform and the number of payments is an odd number.
So logically, the answer we have got in question 4 is its 3rd payment installment.

1st payment = 34646.22 / ( 1.06 ^ 2 ) = 30835.012
2nd payment = 34646.22 / 1.06 = 32685.113
3rd payment = 34646.22
4th payment = 34646.22 * 1.06 = 36724.993
5th payment = 34646.22 * ( 1.06 ^ 2 ) = 38795.92

Alternatively,

x+(x*(1.06))+(x*(1.06)^2)+(x*(1.06)^3)+(x*(1.06)^4) = 173231.1
solving for x gives us approximate value of 30730.55