How do I solve this question?
I'd like to know how to make a formula!
An investment is expected to produce a uniform continuous rate of money flow of $500 per year for 10 years. Find the present value at 9% compounded continuously.
How do I solve this question?
I'd like to know how to make a formula!
An investment is expected to produce a uniform continuous rate of money flow of $500 per year for 10 years. Find the present value at 9% compounded continuously.
To make your formula, you just need to determine the effective rate of 9% compounded continuously. To refresh your memory, by effective rate, I am of course referring to the nominal rate compounded annually. Once you have determined that, you merely plug that rate to the standard present value annuity formula(s), i.e. beginning of year payment version or end of year payments version, depending on what you mean by $500 per year for 10 years.
For the end of year payment version, you should have
$\displaystyle
\sum\limits_{t = 1}^{10} {500e^{ - 0.09t} } \approx \$ 3,150.702702...
$
You can now easily derive a formula from the preceding statement if you’re already familiar with geometric series, as I’m sure you are.
If you wish to avoid the sigma notation (and see the formula itself using the 1st hint I gave you earlier),
see my post at S.O.S. Mathematics CyberBoard :: View topic - Continuous compounding of interest
For the beginning of year payment version, you should have
$\displaystyle
\sum\limits_{t = 0}^9 {500e^{ - 0.09t} } \approx \$ 3,447.417872...
$