Somehow the formula you derived for S(t) is not correct. Because you are using continuous compounding, the interest rate r should be adjusted. In Engineering Economy, we convert the interest rate r which is the nominal interest rate into effective interest rate. In this case, the effective interest rate will be (e^r - 1). The term k/r will replace with k/(e^r - 1) in the above formula for S(t).
@@ProfJeffreyChasnov The error in the formulation is in the r(delta t)S(t) term. r and delta (t) are not compatible with each other. r is an annual value whereas delta t approaches 0. r will be different for different t values. Similarly, k is a discrete value at specific intervals. The correct formula from engineering economy will be S(t) = S0(e^rt)+k[(e^rt - 1)/(e^r -1)].
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Thanks
Thank you! This helped a lot. I was stuck setting up the DE. have a great day
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What if you take any money out of that account? Would you make a new variable and multiple it by t and subtract it from s(t).?
what would be the formula for a FV of a forward contract with a dividend pay in between?
how about the general form of compound interest, dS/dt = p(t)*S + f(t), S(0) = S_0
Is it me or is the audio getting ahead than the video? Oh i had it backwards
Somehow the formula you derived for S(t) is not correct. Because you are using continuous compounding, the interest rate r should be adjusted. In Engineering Economy, we convert the interest rate r which is the nominal interest rate into effective interest rate. In this case, the effective interest rate will be (e^r - 1). The term k/r will replace with k/(e^r - 1) in the above formula for S(t).
r is the continuous compounding interest rate.
@@ProfJeffreyChasnov The error in the formulation is in the r(delta t)S(t) term. r and delta (t) are not compatible with each other. r is an annual value whereas delta t approaches 0. r will be different for different t values. Similarly, k is a discrete value at specific intervals. The correct formula from engineering economy will be S(t) = S0(e^rt)+k[(e^rt - 1)/(e^r -1)].
@@arialcad The answer is correct. You can proof it by integrating both sides (dS/dt-rS) and k.