Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

An amount of $1000$ is to be accumulated at a compound rate of discount of $9$% per year. (a) Find the present value $3$ years before (b) Find the value of i corresponding to d.

For a) i have done the following: $1000=X(1-0.09)^{-3}$


I am not sure on how to go on about (b).

share|cite|improve this question
For (a), did you mean $1000=X(1-0.09)^3$? I'm not sure if I understood it... What are i and d in (b)? – Guest 86 Jan 24 '13 at 23:11
i used (-3) because they said to find the present valye 3 years "before". the before part has confused me – Yenny Chen Jan 24 '13 at 23:17
d=0.09 and i is what we need to find – Yenny Chen Jan 24 '13 at 23:18
Guest86 is asking what the variable $i$ represents, not what its value is. Apparently $d$ is the discount rate, but what is $i$ supposed to represent? – Austin Mohr Jan 24 '13 at 23:33

EDIT: This answer is probably incorrect. It is left up in order for OP to provide clarification.

If you have \$1000 now and you want to know the value three years prior, \$1000 is your initial value. The relevant computation is therefore $$ 1000(1 - 0.09)^{-3} \approx 1327.01. $$

An alternative approach is to say I have an initial value of $X$ that will be worth \$1000 in three years. In this case, you would solve $$ 1000 = X(1 - 0.09)^3 $$ and find $X \approx 1327.01$.

share|cite|improve this answer
If you want the value three years ago, it should be less than \$1000, as there has been some interest since then to get to \$1000 – Ross Millikan Jan 24 '13 at 23:54
@RossMillikan I mistook "rate of discount" to be "rate of depreciation". Should we instead be using $1 + 0.09$, or is discount something else entirely? – Austin Mohr Jan 25 '13 at 0:44
I suspect so, but am confused between discount rate and interest rate. – Ross Millikan Jan 25 '13 at 1:18

For (b), it would seem to me that what you seek is a value of interest $i$ such that

$$1+i = \frac{1}{1-d}$$

where $d$ is the depreciation. This then means that

$$i=\frac{d}{1-d} = \frac{0.09}{0.91} \approx 0.0989$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.