Tricks for Calculating compound Interest with More intervals

Question

What is the trick to solve compound interest questions which have more intervals of interest calculation>

Example. .. What is the balance in Mr XYZ's account after 5 years if at the beginning he invest $100 at 15% compounded semi-annually?

philipssonicare · Answer

What is the balance in Mr XYZ's account after 5 years if at the beginning he invest $100 at 15% compounded semi-annually?

FV=PV(1+\frac{r}{m})^(mn)

FV=future value
PV=present value
r=interest rate (expressed as a decimal)
m=periods per year (the 'intervals' that you mentioned)
n=years

FV=100(1+\frac{0.15}{2})^(5·2) 
 FV=100(1.075)^10 
FV=206.1031562

Clearly this is too complicated to solve in 2 minutes (or at all, really). I don't think I have come across this in GMAT.

vamkrispk · Answer

I had got a similar question in one of the mock tests i have written.. so i got worried.. thank you for the response :D

EMPOWERgmatRichC · Answer

Hi vamkrispk,

If a GMAT question asks you to calculate interest more than once a year, you have to make some minor changes to the Interest Formula (specifically to the interest rate and the number of time-periods).

For example, $1,000 invested at a 10% Compound Interest Rate for 2 years would be:

($1,000)(1.1)^2 = ($1,000)(1.21) = $1,210

If in that same situation, you were asked to calculate interest SEMI-ANNUALLY (meaning TWICE per year), you would then have to cut the interest rate in HALF and DOUBLE the number of time periods:

($1,000)(1.05)^4

It's unlikely that the GMAT would actually require that you to calculate this type of result, but you could do it if needed. It's worth noting that when calculating interest more than once per year, the total amount at the end of all the calculations will be GREATER than if you calculated just once a year (this is generally referred to as "interest on top of interest.").

($1,000)(1.05)^4 = $1,215.51

If you came across a specific Interest Rate question during your studies, then there's a pretty good chance that it's been discussed in the forums here, so you might try "Googling" the question to see if it's been discussed.

Beyond this Quant issue, if you're looking for any additional advice for your studies, then it would help if you could provide a bit more information on how you've been studying and your goals:

Studies:
1) How long have you studied? How many hours do you typically study each week?
2) What study materials have you used so far?
3) How have you scored on EACH of your CATs (including the Quant and Verbal Scaled Scores for EACH)?
4) What is your overall goal score?
5) When are you planning to take the GMAT?

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

To keep things simple, we can go step by step:

1) What is the interest of 100 at 15% for one year? It is 100*(15/100)

2) What is the interest of 100 at 15% for six months? It is half of the figure above i.e. 100*(15/100)*(1/2) = 100*(15/200)

3) What is the total amount at the end of six months? It is principle plus the interest we calculated above i.e. 100 + 100*(15/200) = 100(1 + 15/200)

4) Compound interest means at end of the second six months, you get interest for not just your principal of $100, but instead you get interest for the total amount at the end of six months, which we just calculated above. Notice that the total amount is found simply by multiplying (1 + 15/200); therefore, at the end of the second six months, you’ll have 100*(1 + 15/200)*(1 + 15/200) = 100(1 + 15/200)^2.

5) To find the value at the end of third, fourth, fifth etc. six months, you just keep multiplying by (1 + 15/200). Since in 5 years there are 10 six month periods, the total amount at the end of 5 years will be 100(1 + 15/200)^10.

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Tricks for Calculating compound Interest with More intervals

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