Ask Me Help Desk - NPV and Annuity Maths Help

The total sum is given by the formula:

$Money = P(1+ \frac{r}{n})^{nt}$

The sum of money of Mr Jones is then:

$Money = P(1+ \frac{0.06}{72})^{72(6)}$

That of Mr. Smith now.

After a month, he has {900(1 + 0.06/12) + 900}
After two months, he has [{900(1 + 0.06/12) + 900}(1 + 0.06/12) + 900]
After three months [{900(1 + 0.06/12) + 900}(1 + 0.06/12) + 900](1+0.06/12) + 900

The pattern is:
0. P
1. $P(1+\frac{r}{12}) + P$
2. $(P(1+\frac{r}{12}) + P)(1+\frac{r}{12}) + P = P(1+\frac{r}{12})^2 + P(1+\frac{r}{12}) + P$
3. $(P(1+\frac{r}{12})^2 + P(1+\frac{r}{12}) + P)(1+\frac{r}{12}) + P = P(1+\frac{r}{12})^3 + P(1+\frac{r}{12})^2 + P(1+\frac{r}{12}) + P$

Which gives:

$Money\ after\ n\ months = P(1 + (1+\frac{r}{12})^1 + (1+\frac{r}{12})^2 + (1+\frac{r}{12})^3 + ... + (1+\frac{r}{12})^n) = P$\frac{1(1-0.06^{n})}{1-0.06}$$

Which is a geometric progression!

So, after 72 months (6 years), the money of Mr. Smith will be:

$Money = 900$\frac{1(1-0.06^{72})}{1-0.06}$$

Now, this equals to the money of Mr Jones, so we get:

$P(1+ \frac{0.06}{72})^{72(6)} = 900$\frac{1(1-0.06^{72})}{1-0.06}$$

Solve for P.

Post what you tried for the other questions as well as the answer you got for this one.