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A sum of money is to be invested for a 6-year period. which of the following investments will give the greatest return?
A. 9% p.a Simple interest
B . 8.5% p.a. interest compounded annually
C. 8.4% p.a. interest compounded six-monthly
D. 8.25% p.a. interest compounded monthly
E 8.0% p.a. interest compounded quarterly

 May 24, 2021
 #1
avatar+113616 
+1

You need to work out the answer for each and compare them.

 May 24, 2021
 #2
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+1

But how do you work it out?

 May 24, 2021
 #3
avatar+113616 
+1

hi guest, it is nice that you responded.  We often get the feeling we are talking to brick walls.

 

Simple interest is just 

 

interest = P * r * n

 

where P is the principal, that is the amount that you start with.

 

r is the rate, it is easiest to do it as a decimal.

so if the interest rate is  8.4% that is 8.4 divided by 100,  which is 0.084  so in this case r would equal 0.084

 

n is the number of investment periods.  Usually years.  that is what annum means and p.a.  means per annum.

 

So multiply those together to get the interest and then add it to what you started with to get the total amount that you will have at the end.

 

Future value = P + interest

 

-------------------

Compound interest is a little more confusing.  Each time period your interest is added on and then you get interest on your interest as well as on your principal so it works out to be a bigger amount.

 

The formula is

 

FV= P(1+r)^n

 

FV stands for future value

^ means to the power of

r and P and n have the same meaning as before.

 

I'll do C for your:

C. 8.4% p.a. interest compounded six-monthly over 6 years

 

The compounding period is 6 monthly,  Keep that in mind.  There are 2 lots of 6 months in a year.   12/6=2

 

the interest rate is 8.4% for a year but we are interested in 6 months.  So that must be 4.2% in 6 months. (half as long, has the interest)

so  r= 4.2% = 0.042

 

It is over 6 years but how many lots of 6 months is this?    6 years, 2 per year = 12 lots of 6 months.

12 compounding periods

n=12

 

P is what you start with  P, oh we do not have a P.   doesn't matter,  

You are making comparisons so you can either make a P up, like $100, and use it for EVERY question. OR you can just leave it as P for EVERY question.

I'll leave it as $P, at least for now.

 

So Future value =\( P(1+0.042)^{12} = P*1.042^{12} = P*1.63837\)      dollars.

 

 

 

Note, that interest is already included you don't need to add it on at the end like you did for simple interest.

 

After you get all your future values you can compare them to see which is bigger.

 

If the P's confuse you just change them all to $100 so it will be easier to compare.  

 

Show me how you go with this.

 May 25, 2021

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