B
bapcki1
Member
Hi,
Hope you are all well!
In the 2013 CT1 Chapter 5 Core Reading there is an example of how to calculate the present value of a five-year continuous cashflow;
\[p(v) = 100 \times (0.8)^t\]
and constant force of interest 8% pa.
I understand why in this particular circumstance I need to integrate I just don't understand this specific example of integration.
Could someone walk me through the following integration to calculate the present value please? i.e which rules of integration have been employed here please?
\[ \int_0^5 (e^{-0.08t} \times 100 \times 0.8^t) dt = 100 \int_0^5 ((e^{-0.08}) \times 0.8)^t = \Bigg [ \frac{100(e^{-0.08} \times 0.8)^t}{log(e^{-0.08} \times 0.8)} \Bigg ]^5_0 \]
Let me know if there is any further information I can be providing.
Many thanks,
Paddy
Hope you are all well!
In the 2013 CT1 Chapter 5 Core Reading there is an example of how to calculate the present value of a five-year continuous cashflow;
\[p(v) = 100 \times (0.8)^t\]
and constant force of interest 8% pa.
I understand why in this particular circumstance I need to integrate I just don't understand this specific example of integration.
Could someone walk me through the following integration to calculate the present value please? i.e which rules of integration have been employed here please?
\[ \int_0^5 (e^{-0.08t} \times 100 \times 0.8^t) dt = 100 \int_0^5 ((e^{-0.08}) \times 0.8)^t = \Bigg [ \frac{100(e^{-0.08} \times 0.8)^t}{log(e^{-0.08} \times 0.8)} \Bigg ]^5_0 \]
Let me know if there is any further information I can be providing.
Many thanks,
Paddy