1. ## Now-value? Summation problem.

This is the problem from the book:

A winner in a lottery can receive 50.000kr(swedish currency) every month for 25 years. The winner wants to know what the prise money is worth today.

a) What monthly interest rate is equivalent of a yearly interest rate of 4%?

b) What is the now-value for the whole prise if we count with a yearly interest rate of 4%?

a) was easy; it's just to take $~\sqrt[12]{1.04}\approx 1.0033~$, which gives the monthly interest rate of 0.33%

b) on the other hand was difficult. I did this calculation $~\frac{50000(\sqrt[12]{1.04}^{300}-1)}{\sqrt[12]{1.04}-1}\approx 25442406~$ to get the now-value.

The correct answer however, acording to the aswers section, is that the now-value is approximately 9.600.000 kr.

What is a now-value? I must obviously have a gross misunderstanding of the word.

2. hasn't your teacher defined these terms before giving you questions on them? The definition varies depending on your area and level of study.

One definition is: The present value of some payments is the amount of money that would need to be set aside now to meet the payments in future.

Your formula is for the acumulated value, not the present value. The formula should be:

$50000 \frac{1 - v^{300}}{i}$

where
$i = 1.04^{1/12} - 1$
$v = 1.04^{-1/12}$

I assume that payments are made at the end of each month. I got an answer of around 9,544,000.

If I assume payments are made at the start of each month (and adjust the formula appropriately) my answer is more like 9,575,000.

3. Yes, I also got the right answer after inverting the monthly interest, but I don't understand why the interest rate should be inverted. And our teacher hasn't gone through the "now-value"-definition for this partcular problem, it's just something I found in my book that I found a bit weird.