If X is invested in a bank at a rate of simple interest of y% p.a. for

Question

If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 800. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 820. What is the value of X?

A. 8000
B. 6000
C. 5000
D. 4000
E. 3000

A. 8000
B. 6000
C. 5000
D. 4000
E. 3000

zhanbo · Accepted Answer

My answer is A. Here is my approach.

Based on the info from the question, we can have the following system of equation. (Note that I interpret y as the interest rate itself)

x * y * 2 = 800
x * (1+y)^2 - x = 820

With some simplification:
xy = 400
2xy + x*y^2 = 820

Further simplification by substituting xy with 400
800 + 400y = 820
So: y = 0.05

And x = 400 / 0.05 = 400 * 20 = 8000

Lampard42 · Answer

The difference between simple and compound interest is interest on interest only. So interest for both simple and compound interest will be the same on first compounding.

Using simple interest PNI=800; PR=400 (N=2).
Based on the above reason 20$ extra is due to interest on interest PI*I=20; 400*I=20; I=20*100/400 and I=5%.

Use I=5% and N=2 in simple interest to obtain Principle P*2*5/100=800= 8000 IMO A

somyamehta777 · Answer

My approach of solving this -

Y1 interest will be same for CI as well as SI i.e. 400
Y2 the extra 20 is what we are earning from CI, which is nothing but SI on interest earned in 1st year 
i.e. (400 * Y * 1)/100 = 20 
From here we get Y = 5%
And hence X -> (8000 by X * 5 *2 )/100 = 800 gives X= 8000

ScottTargetTestPrep · Answer

Solution:
 
Using the simple interest formula (Principal x rate x time = Interest) we have:

X * y/100 * 2 = 800

Xy/50 = 800

y = 40,000/X

Using the compound interest formula  Alternate Solution:

The question mentions no units, so we will use dollars for clarity.

Since the interest is simple, exactly half of the interest of $800 is the annual interest; in other words, the principal of X acquires an interest of 800/2 = $400 in one year.

When the interest is compounded annually, we see that 820 - 800 = $20 more interest is earned. This is because in the second term, the principal acquiring interest is X + 400 dollars instead of X dollars. Thus, the extra interest of $20 is y percent of $400. Let’s use this to calculate y:

400 * y/100 = 20

y = 5

Now that we know y = 5, let’s use the fact that X dollars generate $400 in interest in one year at 5 percent:

X * 5/100 = 400

X = $8,000

Answer: A

adityasuresh · Answer

If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 800. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 820. What is the value of X?

A. 8000
B. 6000
C. 5000
D. 4000
E. 3000

A. 8000
B. 6000
C. 5000
D. 4000
E. 3000

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 (first two years) = Interest on the interest for the 1st year

Now, coming back to the problem in hand
If SI is $800 for 2 years, the simple interest for one year is  $800/2  = $400

Compound interest(2nd year) = $400*2 + Interest on $400 = $20 (820-800)
We can calculate the rate of interest as  20/400 * 100 = 5%. Now, as $400 is the interest for the first year and we have found the rate of interest to be 5%, the principal is  400/0.05  = $8000

A

PSKhore · Answer

The difference in SI and CI for year 2 is always the interest on the interest of the first year.
800 is the interest for 2 years, so for one year, the interest will be 400.

The difference in interests for year 2 is 20 (this is the interest on interest of 400)
20/400 = 5%

5% interest is 400, 10% will be 800, 100% will be  8000 .

If X is invested in a bank at a rate of simple interest of y% p.a. for

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If X is invested in a bank at a rate of simple interest of y% p.a. for

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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