Solving Time value of money

**kelxktyc** · July 1st 2011, 09:34 PM

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.

Thanks in advance!

**Prove It** · July 1st 2011, 09:35 PM

Start by getting a common denominator.

**kelxktyc** · July 1st 2011, 09:38 PM

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.

**Prove It** · July 1st 2011, 09:45 PM

Definitely not by trial and error.

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

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

**kelxktyc** · July 1st 2011, 09:48 PM

Originally Posted by Prove It

Definitely not by trial and error.

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

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?

**Prove It** · July 1st 2011, 09:50 PM

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.

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