How Do You Calculate the Interest Rate for Compound Interest Problems?

[iksotof]

Have this question in relation to some investment exam I am doing, I am a maths novice being some years since leaving school etc, ok enough of the excuses.

Example

FV = future value
PV = present value
R = interest rate
N = number of compounding periods


my PV is 6000 and my FV is 10000. Compounding periods is 12, I need to find the interest rate, thus...

100000 = 6000 (1 + R) to power of 12 (sorry don't know how to represent that on key board).


substitution: 1.67 = (1 + R) power 12


substitution 2: 12√1.67 = 1 + R

1.0435 - 1 = R

R = 4.45.

All very well, but I lose understanding of how the maths is applied at sub 2, my textbook
has given this model answer. For a novice please show me step by step what


12√1.67 means.


Thanks you Darren.

 

[arildno]

Okay, to "cancel" the operation of cubing a number, you need to to take the cube root in order to get back to your number.

That is we have for any number a:
$$\sqrt[3]{a^{3}}=a$$
(Taking the cube root of a cube leaves you with the original number "a")

Similarly, if a positive number "a" is raised to the twelfth power, you must take the twelfth root to get a back:
$$\sqrt[12]{a^{12}}=a.$$

Now, how to use this in your present case`

WEll, you are to solve for R, but that appears in your equation within the expression [itex](1+R)^{12}[/tex]<br /> <br /> Now, you are ALLOWED with an equation to "do" whatever operation you like, AS LONG AS YOU DO THE SAME ON BOTH SIDES!.<br /> <br /> Thus, in order to remove the twelfth power on the right hand side (increasing your chances to solve for R!), you take the twelfth root of both sides.<br /> <br /> <br /> That's what the second substitution does.[/itex]

 

[HallsofIvy]

Have this question in relation to some investment exam I am doing, I am a maths novice being some years since leaving school etc, ok enough of the excuses.

Example

FV = future value
PV = present value
R = interest rate
N = number of compounding periods


my PV is 6000 and my FV is 10000. Compounding periods is 12, I need to find the interest rate, thus...

100000 = 6000 (1 + R) to power of 12 (sorry don't know how to represent that on key board).

Using just the keyboard, 100000= 6000(1+R)^(12). Using "html" tags, 100000= 6000(1+R)¹². Using "LaTex" $100000= 6000(1+ R)^{12}$. But you don't mean "100000" on the left, only 10000.

substitution: 1.67 = (1 + R) power 12

Dividing both sides by 6000, 10000/6000= 10/6= 4/3 which is 1.67 to two decimal places.

substitution 2: 12√1.67 = 1 + R

1.0435 - 1 = R

R = 4.45.

All very well, but I lose understanding of how the maths is applied at sub 2, my textbook
has given this model answer. For a novice please show me step by step what

Thanks you Darren.

12√1.67 means.[/quote]
It means the "twelfth root of 1.67", not "square root"! The "twelfth root of x" is defined as the number whose 12 power is x- that's why $^{12}\sqrt{(1+R)^{12}}= !+R$. To actually do the that on a calculator, if you have a "^", power, key, use the "1/12 power": 1.67 ^ (1/12). If your calculator does not have a "^" key you will need to use logarithms. log(x^{1/12})= (1/12)log x= log x/12. To find the 12th root of 1.67, take the logarithm of 1.67, divide by 12, the use the "inverse" to logarithm: 10^ if you are using common logs

 

[arildno]

$^{12}\sqrt{(1+R)^{12}}$, rather: $\sqrt[12]{(1+R)^{12}}$

 

[iksotof]

Thank you greatly but I am a total novice and whilst I am sure your explanation is clear to a knowledgeable person, I am not, in isolation therefore it doesn't mean a great deal. Could you maybe show the maths in long hand please? For example 2 cubed is 2 x 2 x 2=
8.

Please continue with this long hand through the remainder.


Thanks again Darren.

 

[arildno]

Yes, and tell me:

What is the definition of the cube root of a number?

 

[HallsofIvy]

Thank you greatly but I am a total novice and whilst I am sure your explanation is clear to a knowledgeable person, I am not, in isolation therefore it doesn't mean a great deal. Could you maybe show the maths in long hand please? For example 2 cubed is 2 x 2 x 2=
8.

Please continue with this long hand through the remainder.


Thanks again Darren.

Continue with what? 2³= 8 exactly as you said. If you want us to now find $\sqrt[3]{8}$ (thanks, arildno)? There is no calculation involved. By the definition of cube root, it is 2.

If you were to ask me, "What is the cube root of 7?", I would whip out my calculator and answer that $\sqrt[3]{7}= 1.913$, approximately.

 

[iksotof]

Thank you, it was the fundamental understanding I was being a total dumb ass with. . Thanks for your patience and inputs, my old school lessons are finally reawkening from the recesses of my mind, 20 years on!

Greatly appreciated, Darren.