# Financial math

1. Oct 19, 2006

### ToxicBug

This is a problem on an assignment for my actuarial class.
First of all I found how much time it would take for the investment to reach the present value of the perpetuity:

10000(1 + i)^n = 2000/i
10000(1 + 0.05)^n = 2000/0.05

n = ln(4)/ln(1.05)
n = 28.41339817

Then for the second part I did this:

X + 10000(1.05)^(28.41339817 - 1) = 2000/0.05
X = 1904.7618

But the answer in the back of the book is 1161.36

Anyone know what is my mistake?

2. Oct 19, 2006

do you mean $$10000(1+i)^{t}$$?

3. Oct 19, 2006

### shmoe

The scholarship payments aren't starting at year 28.41339.... Year 29 is the first year you have enough to sustain the perpetuity, the first payment is at year 30 though. The excess payment would be at year 29.

4. Oct 19, 2006

### ToxicBug

Brilliant, thanks!!!

5. Oct 19, 2006

### ToxicBug

Another question if you don't mind, I would like to get a hint on what I'm supposed to do:

6. Oct 19, 2006

$$P = P_{0}e^{rt}$$

7. Oct 19, 2006

### ToxicBug

Tried that, didn't work.

8. Oct 20, 2006

### ToxicBug

Any ideas?

9. Oct 20, 2006

### physics girl phd

there are two things involved each year -- a 4% growth, but a subtraction of \$2300... seems like your first try only took into account one of those. Any ideas on how to stick in the other?