Question

A ski chalet at Peak n' Peak now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Chris and Julie retire from successful investment banking careers.

 a. What is the expected cost of the chalet if its price increases at the rate of inflation over the next ten years?

 b. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 11 percent in order to buy the ski chalet upon retirement?

Answer 1

Solution (a)

The following formula will be used for adjustment of inflation into the costs.

Pn = P(1+i)n

Where:

Pn = Total Inflated Estimated Cost

P = Base estimated Cost

i = Inflation Rate

n = Difference between Base Year and Selected Year. Ex 2010-20 = 10 years.

Statement showing the expected cost of the chalet in the 10th year from now. After adjustment 5% inflation each year.

Years	Inflation@5%	Cost
0	00	250000.00
1	12500.00	262500.00
2	13125.00	275625.00
3	13781.25	289406.25
4	14470.31	303876.56
5	15193.83	319070.39
6	15953.52	335023.91
7	16751.20	351775.11
8	17588.76	369363.87
9	18468.19	387832.06
10	19391.60	407223.66

Hence the price of chalet after adjustment of inflation for each year would be $407223.66 at the end of year 10 from now.

This price includes

Basic price as on today = $250000.00

increase due to inflation = $157233.66

Solution (Part 2)

Equal annual deposits can be calculated, the total amount of cost divided by the cumulative discounting factor for 10 years.

Statement showing the calculation of the cumulative discount factor for 10 years @11%

Years	DF@11%
1	0.900
2	0.812
3	0.731
4	0.659
5	0.593
6	0.535
7	0.482
8	0.434
9	0.391
10	0.352
Total cumulative	5.889

Therefore Equal annual deposits would be:

$407233.66 divided by 5.889 is Equal to =$69150 (Approximately) each year.