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RenB
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A sum of $10,000 invested for two years at the same rate of interest o 23 Aug 2023, 17:59
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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75% (hard)

Question Stats:

67% (02:50) correct 33% (03:11) wrong based on 369 sessions

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A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?

A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
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E
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KarishmaB
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A sum of $10,000 invested for two years at the same rate of interest o 25 Aug 2023, 00:48
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RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?
A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
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In 2 years, the only difference between C and S will be the extra interest earned on first year's interest in case of compound interest.
Ratio C : S = 11: 10

If every year, interest earned in case of simple interest is 5 each, in case of compound interest, 5 was earned both years but an extra 1 was earned in the second year. This 1 was earned on the 5 earned last year and hence rate r = 20% (that is 1/5 * 100)

In case of compound interest,

\(Amount = 10,000 (1 + \frac{20}{100})^2\)
Amount = 14400

Then compound interest = 14400 - 10,000 = 4400

Answer (E)
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ManikSingh
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A sum of $10,000 invested for two years at the same rate of interest o 05 Sep 2024, 05:15
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­C = 1.1 * S
S = (10000 * 2 * r)/100 => 200r
So, C = 220r
Find a multiple of 220 in the answer. :)­
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JoeKan1234
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A sum of $10,000 invested for two years at the same rate of interest o 07 Sep 2024, 02:17
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RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?

A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
Show more
­Compound interest in the first year:

10,000*r% = 100r

So accumulated amount = 100r + 10,000

Compound interest in the second year:

(100r + 10,000)*r% = 100r + r^2

Total compound interest thoughout the 2 years (C) = 100r + 100r + r^2 = 200r + r^2

Total simple interest thoughout the 2 years (S) = 10,000*2*r% = 200r

(200r + r^2)/200r = 11: 10

r = 20

So C = 200*20 + 20^2 = 4400

Answer is E­
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A sum of $10,000 invested for two years at the same rate of interest o 09 May 2025, 02:00
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For the options given currently, can we quickly eliminate on the basis of C being a multiple of 11?
KarishmaB
RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?
A. $1000
B. $1200
C. $2000
D. $2400
E. $4400

In 2 years, the only difference between C and S will be the extra interest earned on first year's interest in case of compound interest.
Ratio C : S = 11: 10

If every year, interest earned in case of simple interest is 5 each, in case of compound interest, 5 was earned both years but an extra 1 was earned in the second year. This 1 was earned on the 5 earned last year and hence rate r = 20% (that is 1/5 * 100)

In case of compound interest,

\(Amount = 10,000 (1 + \frac{20}{100})^2\)
Amount = 14400

Then compound interest = 14400 - 10,000 = 4400

Answer (E)
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A sum of $10,000 invested for two years at the same rate of interest o 21 May 2025, 04:51
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Bunuel please explain , without assuming 20% if we just go with what information is given how to solve
RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?

A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
Show more
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Bunuel
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A sum of $10,000 invested for two years at the same rate of interest o 21 May 2025, 05:07
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shubhim20
Bunuel please explain , without assuming 20% if we just go with what information is given how to solve
RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?

A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
Show more
The solution does not assume r = 20%. It derives r = 20% based on the given ratio C : S = 11 : 10. Please review the solution again.
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A sum of $10,000 invested for two years at the same rate of interest o 16 Oct 2025, 23:20
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A quicker way would be to use the ratios to your rescue to solve this under a min:

Given Ratio of C$:S$ = 11:10 - Glance through the options and we notice that the interest amounts are in 1000s, so multiply the ratio by 100 i.e. 1100: 1000 is now the ratio.

Now test which number fits after multiplying the ratio from 1-9

1. 1100:1000*2 = 2200 :2000 (2200 is not in the option)
2. 1100:1000*3 = 3300 : 3000
3. 1100:1000*4 = 4400:4000 (perfect 4400 is an answer so mark E)

RenB
A sum of $10,000 invested for two years at the same rate of interest of r% per annum, can earn $C of compound interest, compounded annually, and $S of simple interest. If ratio of C to S is 11: 10, what is the value of C?

A. $1000
B. $1200
C. $2000
D. $2400
E. $4400
Show more
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