Compute the present value of a payment of 10 000 Euro after 3 years, if the continuously compounded interest rate in the first year ist 4%, in the second year 6%, and in the third year 5%.
For a continously compounded model we write: $P_0= P(t)e^{-rt} $ So the present value must be $ P_0= \frac{10 000}{e^{0.15}} =8607.08 $ Euro
Is that the correct formula/way for this exercise? I´m not sure..
From what I can see it's correct:
$$ P_3 = P_0 \underbrace{\cdot e^{r_1} \cdot e^{r_2} \cdot e^{r_3}}_\text{one factor per year} = P_0 \cdot e^{r_1 + r_2 + r_3} = P_0 \cdot e^{0.15} \\ P_0 = P_3 \cdot e^{-0.15} \approx 8607.08€ $$