Interpreting a Question...

[IndefatigableLover]

Find the dimension of a triangle whose base is half of its height plus 10cm if the area of the triangle is 65cm^2.

I'm having trouble interpreting the question which is frustrating me >.<

[abeybaby]

and solve

[IndefatigableLover]

and solve

Thanks

[IndefatigableLover]

Another quick question...

A= P(1+r/100)^n

Where:
A=Amount
P= Principal
R= Compound Interest
N=Number of years
 
If the interest is 7% p.a., find the time it takes (to the nearest year) for the principal $P to double in value.

[TrueTears]

Alright firstly just to clarify a few things, try to remember this form of the compound interest formula:



Now it is very important that you clearly distinguish what PV, i, n and FV means

PV is the principal or starting capital that you have.

i is the effective rate per period (note there are 2 types of rates, effective and nominal, i will distinguish this in some examples below)

n is the number of periods

and FV is the future accumulated value of the starting capital.

First, limme give you an example of how this works, say you are given $1000 and you invest this in the bank at an effective rate of 5% p.a for 10 years. How much money do you have after 10 years?

Simple, just

Now what if i said you are given a nominal rate of 5% p.a compounded semi annually for 10 years, the entire question changes.

Note that a nominal rate = effective rate per period * number of periods per year. Thus a 5% nominal rate p.a compounded semi annually means an rate of 0.05/2 = 0.025 per 6 months. Now if we choose 1 period as 6 months, we have 10*2 = 20 periods.

So we have

Now there is another way to do the above, we can convert between nominal annual rates and effective annual rates, the formula (which i give without derivation) is


i = effective annual rate and is the nominal annual rate compounded p times per year. Note that does not mean i raised to the power of p, it is the conventional financial/actuarial notation to represent nominal rates.

So 0.05 nominal rate p.a compounded semiannually is equivalent to effective rate p.a

Thus our accumulation of 1000 becomes

same number as expected just using a different method, but illustrating a very important fact that you must know how the formula works and not just simply plug in numbers, the compound interest "formula" is very very very flexible.

A funny point arises because banks often quote nominal rates and not effective rates, so if the bank quotes you a 10% borrowing rate (nominal) they are actually charging you more than 10%, most people think the rate is good, but when you invest a huge amount, you must work in effective terms never nominal!

As for the question, we need to solve the following equation: Assuming 7% is the effective annual rate.



years

[IndefatigableLover]

Holy crap that was a long explanation.. and one that made sense too
Thanks