Purdie Ltd expects to have to buy a new plant and equipment with a current value of 800,000 pounds in four years time. If currently has 200,000 in a sinking fund paying 6.7% per annum. What equal amount should it set aside into the fund each year if inflation is expected to increase the cost of the plat and equipment by 2% per annum?

I am struggling with this question in terms of starting it out and sorting out methods!

I hope u can help me, as I will be soooo grateful!

The plant and equipment currently cost 800k. In four years time, with inflation, they'll cost

800,000*1.02^4=865,945.72.

Meanwhile, the 200k currently in the fund will be worth

200,000*1.067^4=259,231.44

after 4 years. So at that time Purdie Ltd will need to have saved an additional

865,945.72-259,231.44 = 606,714.28

pounds in order to pay for the new plant and equipment.

So now you simply need to calculate how to raise that sum in four easy payments:

A=P\left[\frac{i}{(1+i)^n-1}\right]=606714.28\left[\frac{0.067}{(1.067)^4-1}\right]=137257.70

This assumes that each payment is made at the end of the year. In other words, the first deposit of that amount is one year from today, and the last deposit is made four years from today - the day that the new plant will be purchased.

The plant and equipment currently cost 800k. In four years time, with inflation, they'll cost

800,000*1.02^4=865,945.72.

Meanwhile, the 200k currently in the fund will be worth

200,000*1.067^4=259,231.44

after 4 years. So at that time Purdie Ltd will need to have saved an additional

865,945.72-259,231.44 = 606,714.28

pounds in order to pay for the new plant and equipment.

So now you simply need to calculate how to raise that sum in four easy payments:

A=P\left[\frac{i}{(1+i)^n-1}\right]=606714.28\left[\frac{0.067}{(1.067)^4-1}\right]=137257.70

This assumes that each payment is made at the end of the year. In other words, the first deposit of that amount is one year from today, and the last deposit is made four years from today - the day that the new plant will be purchased.

You are simply amazing!!
I officially understand this!
Thank u sooo much. I really appreciate the help!!