Seite 205, Nr. 16:
K0 =
23.310,00 EUR
nachschüssig
r = 2.400,00 EUR
q = 1,06
En = 0,00 EUR
n = ? Jahre
Ansatz:
0 = 23.310 * 1,06n - [2.400 * (1,06n
- 1) / (1,06 - 1)]
| 0 = 23.310 * 1,06n - [2.400 * (1,06n - 1) / (1,06 - 1)] | + [2.400 * (1,06n - 1) / (1,06 - 1)] |
| 2.400 * (1,06n - 1) / (1,06 - 1) = 23.310 * 1,06n | / 2.400 |
| (1,06n - 1) / (1,06 - 1) = 23.310 / 2.400 * 1,06n | * 0,06 |
| 1,06n - 1 = 23.310 / 2.400 * 0,06 * 1,06n | / 1,06n |
| (1,06n - 1) / 1,06n = 23.310 / 2.400 * 0,06 | |
| (1,06n / 1,06n) - (1 / 1,06n)= 0,58275 | - 1 |
| - (1 / 1,06n) = - 0,41725 | * (- 1) |
| 1 / 1,06n = 0,41725 | * 1,06n |
| 1,06n * 0,41725 = 1 | / 0,41725 |
| 1,06n = 2,3966... | log |
| n * log (1,06) = log (2,3966...) | / log (1,06) |
| n = 15,000619... |
n = 15 Jahre