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#1 2007-06-03 22:53:20

Identity
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Registered: 2007-04-18
Posts: 934

Comparing interest rates

Three people invest 20000 for 10 years. Sam decides to invest in a 8% p.a simple interest account. Simon decides to invest in a 6% account, compounding monthly. Ben decides to invest in a 6.5% p.a compound interest account. Explain the benefits and disadvantages of each investment.

This right?



Now how do I explain advantages and disadvantages of each?

Last edited by Identity (2007-06-04 01:26:28)

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#2 2007-06-04 01:24:22

George,Y
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Registered: 2006-03-12
Posts: 1,379

Re: Comparing interest rates

Basically yes, but 12 should be replaced by 4 because of the word "quaterly".


X'(y-Xβ)=0

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#3 2007-06-04 01:26:11

Identity
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Registered: 2007-04-18
Posts: 934

Re: Comparing interest rates

Sorry, it was a typo in the question big_smile! Anyway if this were in a test would you just graph the equations and draw the graph on the paper or solve with logs?

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#4 2007-06-04 01:36:15

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Comparing interest rates

There really is no advantage whatsoever in the simple-interest investment. 8% may look “higher” than 6% or 6.5%, but as you have computed, this is least profitable of the three ventures.

Of the two compound-interest investments, obviously the one that yields the more profit is the more advantageous, and that’s the 6.5% one, with interest computed yearly. The other one, with interest computed monthly, has no real advantage other than a psychological one: some people are just happier to see their money growing on a monthly basis rather than a yearly one.

Last edited by JaneFairfax (2007-06-04 02:53:24)

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#5 2007-06-04 03:08:12

George,Y
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Registered: 2006-03-12
Posts: 1,379

Re: Comparing interest rates

But, how can you draw a graph of 1.065^x without knowing the values?
I guess you have gotten a table already, to help you calculate interest rate.

It simply depends, Jane.
Given the total time, a high simple interest rate can beat up a low compound interest-rate.
And typically monthly savings is less profitable than annual savings, because you pay more for the latter-you pay the promise of not withdrawing it for a Whole year.


X'(y-Xβ)=0

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#6 2007-06-04 03:41:20

Identity
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Registered: 2007-04-18
Posts: 934

Re: Comparing interest rates

Say if you were to analyse Ben and Simon's investments without regard to the 10 year period.
If I were to prove that Simon's is better than Ben's, would this be a good way of explaining it?
Since there is no intersection between the two graphs, we know that one investment is always greater than the other. Next, choose a test point, say x = 10, then we know that Simon's is better.

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#7 2007-06-04 14:07:36

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Comparing interest rates

No, after one year or two, Ben's is still better than Simon's-that's why I said it depends.
Ben's curve is a linear one with a good beginning, while Simon's is an exponential one with a poor beginning. In the long run, first interest of the latter will meet the former or even overnumber the former and then keep increasing the gap, after a while the total sum of money of the latter will drawf the latter.

However, "the total sum" does not count in reality. Today's one dollar is different than that after a year. Because bank and interest rate exist.
100today=100(1+interest rate) next year
100/(1+interest rate)=100 next year.
Under this consideration, we can transfer the cash gains of respective years all to equivalent gains today and sum them up, to so called Present Value. And if the compound rate 6.5% is less than the bank interest rate, there is no guarantee for it to beat the annual earnings.


X'(y-Xβ)=0

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