# Financial Mathematics

• Apr 18th 2010, 02:48 PM
bhuang
Financial Mathematics
This problem is in the sequences and series review section of my book, so could someone help me with the problem using sequences and series concepts?

Michele invested 1500 francs at an annual rate of interest of 5.25 per cent.
a) Find the value of Michele's investment after 3 years. Give your answer to the nearest franc.
b) How m any complete years will it take for Michele's investment to double in value?
c) What should the interest rate be if Michele's initial investment were to double in value in 10 years?

What I did was...
a) 1500 x 1.0525^2 = $1662 (which is incorrect, the book has it as:$1749
b) I got the correct answer: 14 complete years
c) 3000 = 1500r^9
r=1.08
Therefore, the interest rate is 8% (which is incorrect, the book has it as: 7.18%)

What did I do wrong, and what are the correct steps to the solutions? Thanks!
• Apr 18th 2010, 04:00 PM
Debsta
Quote:

Originally Posted by bhuang
This problem is in the sequences and series review section of my book, so could someone help me with the problem using sequences and series concepts?

Michele invested 1500 francs at an annual rate of interest of 5.25 per cent.
a) Find the value of Michele's investment after 3 years. Give your answer to the nearest franc.
b) How m any complete years will it take for Michele's investment to double in value?
c) What should the interest rate be if Michele's initial investment were to double in value in 10 years?

What I did was...
a) 1500 x 1.0525^2 = $1662 (which is incorrect, the book has it as:$1749
b) I got the correct answer: 14 complete years
c) 3000 = 1500r^9
r=1.08
Therefore, the interest rate is 8% (which is incorrect, the book has it as: 7.18%)

What did I do wrong, and what are the correct steps to the solutions? Thanks!

In both a and c you have used the wrong time. In (a) you should use 3 not 2, in (c) use 10 not 9.
If you are using the a x r^(n-1) formula, you need to be careful with what n is. Draw a timeline.
• Apr 18th 2010, 08:42 PM
Dr Zoidburg
For part c, you need to find the following:
$1500*r^{10} = 3000$
A bit of simple arithmetic gives us:
$r^{10}=2$
taking the log of each side:
$10log(r) = log 2$
which simplifies to
$log(r) = \frac{log 2}{10}$
take the inverse log of this gives you the answer 1.07177: 7.18% interest.