fdp word bank #3 compound interest

[guest612]

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?


1-if using the formula as stated in answer, i get a different result from the latter approach using A=P(1+r/n)^nt
which is 100=P(1.04)^1. is the math incorrect?

2-the second approach is very intuitive and simple. how then would this be solved for a simple interest problem (versus it being compounded quarterly as in this problem)?

thank you!

[tkkishore]

100 = P (1 + 2/100)^ 2

2/100 because we are given 8% Annual rate and since compounding quarterly, you get 2% quarterly rate.
Since problem is seeking 100$ compound interest in 6 months, which is 2 quarters, you raise (1 + RT/100) portion by power of 2.

[brian]

Thanks tkkishore!
-Brian Lange

[guest612]

Thanks! I appreciate it.

unfortunately i must be doing something blatantly wrong but doing it this way doesn't seem to yield the same result of 2500 which is the answer.

100=P(1+2/100)^2. For some reason I can't use that to get to 2500. Can you please tell me what I'm doing wrong?

Thank you very much.

[StaceyKoprince]

Almost but not quite. The number on the left-hand side of the equation should be the principal PLUS the interest:
P+100 = P(1+ 2/100)^2

So both of the above suggested equations aren't right. Try again with the above.

In addition, the first offered equation:
100=P(1.04)^1
is also incorrect because it imposes a flat 4% rate not compounded at all (compounding something once is the same thing as saying it isn't compounded).

If you're given an annual interest rate and told to compound for some shorter amount of time, keep it in terms of the year. In this case, divide by 4 to get the 2% interest rate per quarter, and then compound it twice to get the interest after six months.

p.s. please make sure to post in correct folder - MGMAT Math Guides in this case :)

[guest612]

stacey, thanks very much for clarifying that!

i'll note the postings more carefully!

[rfernandez]

You're welcome and thanks.

[elevinty]

there is something here that is confusing me..
.the questions asks the minimum amount that will give us an interest ABOVE 100$. According to the OA 2500 will give us exactly 100$ interest; Therefore, shouldn't we choose 3000$ as a principal to get an interest OVER 100$
????

[jnelson0612]

there is something here that is confusing me..
.the questions asks the minimum amount that will give us an interest ABOVE 100$. According to the OA 2500 will give us exactly 100$ interest; Therefore, shouldn't we choose 3000$ as a principal to get an interest OVER 100$
????

Please check out Stacey's explanation. Because we are compounding quarterly we will get a tiny bit more interest than if we were doing simple compounding once a year.

[pratik.munjal]

I am still not sure why the equation has been raised to the power of 2. Perhaps you can explain that using different scenarios-in this case the time frame was 6 months, what is to be done if it is 12 months, 18 months, 24 months etc?

[StaceyKoprince]

the exponent represents the number of periods over which the compounding happens. In this problem, we're told that the interest compounds quarterly, which means every 3 months (3 months = 1 quarter of a year). The problem also asks about a period of 6 months, so that's 2 periods of 3 months each. If the problem had asked about 12 months, we'd have used an exponent of 4, because there would be 4 periods of 3 months each, and so on.