## Compound Interest

Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.
Ian
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### Compound Interest

My calculations below are not included on the list of possible answers.

John borrowed money from Stan. He has to pay Stan R500 three months from now and R930 five months from now. Stan charges him an interest rate of 20% per annum, compounded monthly.

John decides to pay Stan back what he owes him two months from now. How much interest will he save?

[1] \$1376.81
[2] \$430.00
[3] \$53.19
[4] \$97.96

My calculation:

$P = S/(1 + R)^t$
$S= 1430$
$R= 20%/12 = 0.016667$
$T= 8-2= 6$

$P= 1430/(1+0.016667)^6$
$= 1294.98$

Thus the interest saved is $1430-1294.98 = 135.02$. But this seems to be incorrect and I can't find what I'm doing wrong. Please could someone assist me?

stapel_eliz
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John borrowed money from Stan. He has to pay Stan R500 three months from now and R930 five months from now. Stan charges him an interest rate of 20% per annum, compounded monthly. John decides to pay Stan back what he owes him two months from now. How much interest will he save?
In "real life", there are very specific (and often complicated) rules for this sort of thing. For this particular exercise:

If John pays back only the 500 and the 930, then (assuming the amount borrowed was 1430) no interest has been paid. What are the rules for the interest owed, and the schedule on which it is to be repaid? (Mortgages, for instance, "front-load" interest payments.) Is there any pre-payment penalty? Is John allowed to cut the interest paid by paying back early? Is the interest calculated on the entire amount, the amount left owing, or something else?

Ian
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Joined: Tue Feb 25, 2014 8:02 am
Contact:

### Re: Compound Interest

I copied the text verbatim from the textbook. I'm aware of all the possible "real life" variables that may form part of the equation, but in this instance I suppose it's a bit more elementary. I'm really just hoping someone can tell me whether I'm wrong or right in my calculation.

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Joined: Sun Feb 22, 2009 11:12 pm

### Re: Compound Interest

John borrowed money from Stan. He has to pay Stan R500 three months from now and R930 five months from now. Stan charges him an interest rate of 20% per annum, compounded monthly.

John decides to pay Stan back what he owes him two months from now. How much interest will he save?

My calculation:

$P = S/(1 + R)^t$
So P is amt paid, S is principal, R is annual rate, t is years?
$S= 1430$
$R= 20%/12 = 0.016667$
$T= 8-2= 6$
What is T? What is 8-2 for?

$P= 1430/(1+0.016667)^6$
$= 1294.98$

Thus the interest saved is $1430-1294.98 = 135.02$.[/quote]
Is your answer for the amt paid at the end of the whole time? I don't see how you did anything with the part payback. Where did you do a comparison between the two ways of paying? How are you getting that he pays back less than he borrows?

Try using the compound-interest formula: A = P(1 + r/n)^(nt) where A is amt paid, P is principal, r is annual rate, n is compoundings per annum, t is years.

Find amt paid for 1430 at 20% for 3/12 yrs. Find amt paid for 930 at 20% for 5/12 yrs. Add to get total paid for 1st way.

then find amt paid for 1430 at 20% for 2/12 yrs to get total paid for 2nd way. Then compare to find how much he saves.