# Thread: Solving Time value of money

1. ## Solving Time value of money

Hi all,

I'm currently preparing for CFA lvl 1 exams. My maths got rusty. Although it is allowed to use financial calculator, i want to know how to solve this manually, here goes...

(100/(1)) + (100/(1+r)^1) + (100/(1+r)^2 = 250

Solve R.

2. ## Re: Solving Time value of money

Start by getting a common denominator.

3. ## Re: Solving Time value of money

Originally Posted by Prove It
Start by getting a common denominator.
Hi, do you mean via trial and error?

Can show me how is it done?

Many thanks.

4. ## Re: Solving Time value of money

Definitely not by trial and error.

\displaystyle \displaystyle \begin{align*} 100 + \frac{100}{1 + r} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2}{(1 + r)^2} + \frac{100(1 + r)}{(1 + r)^2} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2 + 100(1 + r) + 100}{(1 + r)^2} &= 250 \\ 100(1 + r)^2 + 100(1 + r) + 100 &= 250(1 + r)^2 \end{align*}

Now expand everything, collect like terms, set equal to 0 and solve the resulting quadratic.

5. ## Re: Solving Time value of money

Originally Posted by Prove It
Definitely not by trial and error.

\displaystyle \displaystyle \begin{align*} 100 + \frac{100}{1 + r} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2}{(1 + r)^2} + \frac{100(1 + r)}{(1 + r)^2} + \frac{100}{(1 + r)^2} &= 250 \\ \frac{100(1 + r)^2 + 100(1 + r) + 100}{(1 + r)^2} &= 250 \\ 100(1 + r)^2 + 100(1 + r) + 100 &= 250(1 + r)^2 \end{align*}

Now expand everything, collect like terms, set equal to 0 and solve the resulting quadratic.
Hi, Thanks!

Would you mind show me the rest of the steps to solve R?

6. ## Re: Solving Time value of money

Originally Posted by kelxktyc
Hi, Thanks!

Would you mind show me the rest of the steps to solve R?
Yes I would mind. It is against the rules to complete work for a student that is supposed to count for their grade. You are expected to show some effort.