## Task 1 - 330811

After buying a new car, one must expect a depreciation in value over time. For this depreciation, 20% in the first year, 15% in the second year, and another 15% in the third year are assumed, where all these percentages are based on the original purchase price. The resulting reduced value is referred to as the time value.

a) Mrs. Gruebler paid 23800 DM for her new car. Calculate the time value after two years!

b) Mr. Bauer wants to sell his car after three years. At this point, the time value of the car would be 16200 DM. However, due to an accident, the time value decreases by 10% of this amount.

What percentage of the original purchase price does the resulting reduced time value now represent?

c) Mr. Neumann buys a new car for 43000 DM. He wants to sell the car after four years at the time value, which he assumes to be 18275 DM.

What percentage (of the original purchase price) did he assume for the depreciation in the fourth year?
a) 20% of 23800 DM is 4760 DM, 15% of 23800 DM is 3570 DM.

This results in the value loss of 4760 DM + 3570 DM = 8330 DM.

Thus, the time value is 23800 DM - 8330 DM = 15470 DM.

(With the same reasoning as in b), one can also calculate 100% - (20% + 15%) = 65% of 23800 DM.)

b) Since the percentage values for the value losses are uniformly understood as a percentage of the purchase price, the sum of the value losses is 20% + 15% + 15% = 50% of the purchase price. Therefore, 16200 DM represents the remaining 50% of the purchase price; thus, the purchase price was 32400 DM.

The further reduction in the time value is 10% of 16200 DM, which is 1620 DM. The reduced time value is 16200 DM - 1620 DM = 14580 DM. Since 14580 / 32400 * 100 = 45, this is 45% of the purchase price.

c) 18275 DM is 42.5% of 43000 DM. Again, due to the uniform reference to the purchase price, a percentage of 50% - 42.5% = 7.5% was assumed for the value loss in the fourth year.