User:Didero/Sandbox

vraag4 $$\frac{F}{1+i}=P \quad F=1000, P=800 \to \frac{1000}{1+i}=800 \to 1+i = \frac{1000}{800}=1,25 \to i =0,25=25 \%$$

Vraag 3c $$\frac{1636,18-1136,27}{1136,27} *100\% = 30,55\%$$

Vraag 3b $$P = \sum_{t=1}^n \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n} \quad i=12\%, C=120, F=1000$$

$$P = \sum_{t=1}^{12} \frac{120}{(1,12)^t} + \frac{1000}{(1,12)^{12}} = 743,32 + 892,86 = 1636,18$$

Vraag 3a $$P = \sum_{t=1}^n \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n} \quad i=10\%, C=120, F=1000$$

$$P = \sum_{t=1}^{12} \frac{120}{(1,10)^t} + \frac{1000}{(1,10)^{12}} = 817,64 + 318,63 = 1136,27$$

Vraag 2 $$ F(1+i)^n, F = 1.000.000, n = 5 \rightarrow (1+i)^5 = 1,8 \rightarrow \ 1+i = \sqrt[5]{1,8} = 1,124 \rightarrow i = 0,12 = 12 \% $$

Vraag 1 $$ 1. P = \sum_{t=1}^n \frac{C}{(1+i)^t} = \frac{1100}{1,12} + \frac{1210}{1,12^2} + \frac{1331}{1,12^3} = \frac{1100}{1,120} + \frac{1210}{1,125} + \frac{1331}{1,404} = 982 + 1076 + 948 = 3006 $$