Question

Nabrich-co wants to buy a pipeline for oil transportation after nine years.
The current cost of the pipeline is $200,000. Inflation rate is 5%. Nabrich-co currently has $15,000 in a bank account that pays an interest rate of 14% compounded semiannually. Nabrich-co wants to save on a semiannually basis from now until the day it buys the pipeline.

1. Compute the amount Nabrich-co has to save semiannually.

2. After four years, nabrich-co decided to buy a pump. The current cost of the pump is $30,000. The company also discovered that it needs the pipeline earlier. Both the pump and the pipeline will be bought in two years (end of year 6) Nabrich-co decided to continue its saving on a quarterly basis in the bank account that now pays 12% interest compounded quarterly. How much should the quarterly payments be?

Answer 1

Nabrich co. wants to buy a pipeline worth $200,000 after 9 years.

That means at the end of year 9 it should have an amount of $200,000.

The amount it will recieve from $15000 at the end of year 9 will be :

=15000*(1.07)18/(1.025)18 = $32506.46

Additional amount required = 200000 - 32506.46 = $167,493.5

Let the amount to be saved semi annually be 'x'.

Now, x/1.025 + x/(1.025)2 + x/(1.025)3 + ...... + x/(1.025)18 = 167493.5

Hence x = 11669.26

Now at the end of year 4 the company realises that it needs both pump and the pipeline within 2 years.

Total investment = $200000 + $30000 = $230,000

The value of $15000 investment at year end 4 is as follows :

=15000(1.07)8/(1.025)8

= $21154.31

These savings are continued for 2 years at quarterly compounding at 12%.

Hence number of period = 8

rate = 12/4 = 3%

inflation = 5/4 = 1.25%

Amount received at the end of 2 years :

=21154.31*(1.03)8 / (1.0125)8 = $24262.55

Additional amount required = 230000 - 24262.55 = $205737.5

Let the semi annual saving be 'x'.

Hence, x/(1.0125) + .......+ x/(1.0125)8 = 205737.5

x = $27184.82