Search

A     B     C     D     E     F     G     H     I     J     K     L     M     N     O     P     Q     R     S     T     U     V     W     X     Y     Z




Formulas
All Tests
 Bookstore 
F7 F9 



  Mathematics - Generally 5



This is the Nissan Leaf, the best selling electric car in the world. His data does not interest us so much now, but more its battery, 2017 to 30 kWh growing. More specifically, the battery of the Nissan Leaf is of interest because you can rent or buy it.

Purely mathematical is the question, which is more favorable in the shorter or longer term. Rental prices are graded according to yearly mileage as well as by runtime. Here, actually, only the longest possible of 3 years makes sense. For our example for an electric car we assume a mileage of 15,000 kilometers per year.

Since the prices for the model with 30 kWh still are not published yet, we take the old one with 24 kWh. The ratio of rent to purchase will be similar. The rent would be € 86 per month. On the basis of experience, the estimate of capacity loss is linearly about 2 percent per year. Then, after 10 years, only 80 percent would be present, e.g. a 30 kWh battery falls to 24 kWh.

We would like to exchange then, although we could go on of course. Nissan replaces rented batteries only at 75 percent. Thus, 86 · 12 = € 1,032 are payable each year, € 10,320 in 10 years. In the case of purchase the already paid 5.900 € would be added by the same sum then, makes together 11,800 €. Seen in this way, rent is cheaper. However, if you come from Nissans 75 percent, the rental price rises to € 12,900 and is less favorable.

YearPaidInterest lostPaidInterest lost
1€ 1032€ 5.900
2€ 1032€ 20,64€ 118,00
3€ 1032€ 41,69€ 120,36
4€ 1032€ 62,75€ 122,77
5€ 1032€ 83,82€ 125,22
6€ 1032€ 104,88€ 127,73
7€ 1032€ 125,94€ 130,28
8€ 1032€ 147,00€ 132,89
9€ 1032€ 168,06€ 135,54
10€ 1032€ 189,12€ 5.900€ 138,26
€ 10.320€ 943,90€ 11.800€ 1.151,05

Admittedly, the interest calculation makes it more complicated. However, it seems certain that it will not remain at so low interest rates as nowadays for the next 10 years. We have continuously assumed above- average 2 percent. The higher, the clearer the pendulum turns in the direction of rents, even at zero interest results in about € 1.500 difference.

However, we have assumde a change at 80 per cent remaining capacity. With 75 percent, the advantage is completely in the direction of 'buy', because in the second column are theoretically to be added 2.5 · 1.032 €. This yields 12,900 € in the second column, while in the fourth column everything remains the same.

If the interest is added, the table above shows that the interest in the third column exceeds more than in the fifth column. Who would have thought that the time or remaining capacity plays such an important role in the mathematics of exchange? Incidentally, the influence of the discounting of batteries over time will have an impact on both bills, since the manufacturer has every three years an interest in the continuation of the rental contract.

Hardly any manufacturer, including Nissan, writes in his prospectus or his price list, the remaining capacity he exchanges in the case of rents, but this point is of crucial importance. In addition, there are other advantages of buying the battery: you do not have to transfer a contract when selling the vehicle. You do not have to pay extra charge and must not wait on the OK of the manufacturer.

In both cases, you should say goodbye to the possibility to get more capacity with a new battery because there is often also hardware, which would have to be changed, too. On the other hand, the interest rate would have to be obtained on an exactly calculation at least once a month, which would have strengthened the conclusions.

However, too much mathematics may lead to lose sight of the motor vehicle technology. The question is whether a 12.5-year-old electric car with 187,500 km is still worth the exchange of an expensive battery. In addition, the contracts for renting batteries are covered with a series of mantraps. As always it is worth reading through.







Sidemap - Technik Imprint E-Mail Datenschutz Sidemap - Hersteller