The simple interest for 10 yrs is 6000$ . Compound interest

Question

The simple interest for 10 yrs is 6000$ . Compound interest for 2 yrs is $1400 . What is the rate percentage and principal.

A. 33.33% , 1600
B. 30%. , 1800
C. 33.33% , 1800
D. 66.66% , 1600
E. 66.66% , 1800

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pushpitkc · Accepted Answer

For questions pertaining to simple interest and compound interest, these are a few concepts that come in handy

1. Simple interest is the exact same amount for all the years.
2. Compound interest = Simple interest(for first year)
3. Compound interest - Simple interest(for the first two years) = Interest on the interest for the 1st year.

Now, coming back to the problem in hand
If SI is 6000$ for 10 years, the simple interest for one year is  \frac{$6000}{10} = $600

Compound interest(2nd year) $600*2 + Interest on $600 = $1400 -> Interest on $600 = $200
We can calculate the rate of interest as  \frac{200}{600}*100 = 33\frac{1}{3} %. Now, as $600 is the interest for
the first year and we have found rate of interest to be  33\frac{1}{3} %, the principal is  600*3 = $1800 .

Therefore, the interest rate and the prinicpal are  33\frac{1}{3}%  and  $1800  (Option C)  respectively

SchruteDwight · Answer

Poorly worded question; No compounding periods are given.

swethakandra · Answer

can anyone explain this clearly?

IanStewart · Answer

The wording of this question is awful, and you need to guess what it's even asking. We also don't even need half of the information to answer the question. When interest is "simple", that means the interest applies only to the initial investment every time. So if you invest $5000 at 10% simple annual interest, you earn $500 every year (10% of the initial $5000 investment) -- it never changes, and there is no compounding. So in this question, if the investment earns $6000 in simple interest over a 10 year period, it is earning $600 in simple interest each year. That information alone doesn't let you work out the size of the investment or the interest rate (it could be a $1200 investment earning 50% each year, or a $60,000 investment earning 1% each year, among many other possibilities), but if you look at the five answer choices, only answer C correctly gives us $600 of simple interest in one year. So we don't even need to bother with the information about compound interest.

luisdicampo · Answer

Deconstructing the Question

Simple interest for 10 years is  6000 .

Using:

SI = Prt

6000 = P \cdot r \cdot 10

Pr = 600

For 2 years:

SI_{2} = Pr \cdot 2 = 600 \cdot 2 = 1200

Compound interest for 2 years is  1400 .

For 2 years:

CI - SI = Pr^2

Step-by-step

Difference:

1400 - 1200 = 200

Pr^2 = 200

Substitute  Pr = 600 :

600r = 200

r = \frac{200}{600} = \frac{1}{3} = 33.33\%

Now find principal:

P \cdot \frac{1}{3} = 600

P = 1800

Answer: C

The simple interest for 10 yrs is 6000$ . Compound interest

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The simple interest for 10 yrs is 6000$ . Compound interest

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