Accumulated value using continuous method?

[joelee88]

Hi guys, just have a question and would highly appreciate it if u could please help me with this simple question?

Referring to Question 7.12 Chapter 7, Pg 13 of CT1 07,

A dwarf agrees to make investments continuously for the next 10 years. He decides that he can afford to invest USD 20t at time t, 0</= t </= 10. The annual effective rate of interest throughout the ten years is 3.7%.

Given the PV of 787.82 at time 0, calculate the accumulated value at time 10.

The answer given in the combined pack is 787.82*1.037^10 = 1132.96

My question is, when calculatating the accumulated value, why shouldn't we use force of interest [ln (1+0.037)] instead of the effective interes rate 0.037? Its continuous annuity afterall?

Thanks in advance for your help!

 

[jack93]

This is what I think:
In the questn they have already given the PV which would have been calculated keeping continous payments in mind.
Now that we have the PV, we can directly accumulate it using effective rate per year.
[Note that the PV is not invested continously. Its a single payment which will accumulate using the given interest rate]

If we were to accumulate payments till 10 years (without finding PV), we would have to use the force of int fr accumulation.

I hope this helps

 

[prashanth]

Hi friends,

what you said is correct, and it is also possible to calculate accumulated value using force of interest (log(1.037) = 0.036332). will give you the same answer.

= 787.82* \(e^{0.036332*10}\)

= 1132.96

 

[joelee88]

Alright, got it Thanks a lot guys!