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Q:

A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.

A) 4360	B) 4460
C) 4560	D) 4660

Answer & Explanation Answer: B) 4460

Explanation:

Let the sum be Rs.P.then
P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)
On dividing,we get (1+R/100)^3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.

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Q:

A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent

A) 3400	B) 4400
C) 5400	D) 6400

Answer & Explanation Answer: C) 5400

Explanation:

Interest for 1 year is the same whether it's simple interest or the compound interest.

Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225

if 100 is the principal interest =(1225/7350) * 100 = 50/3 %

When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100

Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount principal =100

if 7350 is the amount principal =(900/1225)*7350 =5400

So sum = 5400; Rate = 50/3 %

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Q:

Divide Rs. 1301 between A and B, so that the amount of A after 7 years is equal to the amount of B after 9 years, the interest being compounded at 4% per annum.

A) Rs.625	B) Rs.626
C) Rs.286	D) Rs.627

Answer & Explanation Answer: A) Rs.625

Explanation:

Let the two parts be Rs. x and Rs. (1301 - x).

$x {(1 + \frac{4}{100})}^{7} = (1301 - x) {(1 + \frac{4}{100})}^{9}$

$\frac{x}{(1301 - x)} = {(1 + \frac{4}{100})}^{2} = (\frac{26}{25} * \frac{25}{26})$

=> 625x=676(1301-x)

1301x=676 x 1301x=676.
So,the parts are rs.676 and rs.(1301-676)i.e rs.676 and rs.625

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Q:

The difference between the compound interest and the simple interest accrued on an amount of Rs. 18,000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?

A) 12%	B) 13%
C) 14%	D) 15%

Answer & Explanation Answer: D) 15%

Explanation:

Let the rate be R% p.a. Then,

$[1800 {(1 + \frac{R}{100})}^{2} - 1800] - (\frac{1800 * R * 2}{100}) = 405$

$1800 [\frac{{(100 + R)}^{2}}{10000} - 1 - \frac{2 R}{100}] = 405$

$1800 [\frac{{(100 + R)}^{2} - 10000 - 200 R}{10000}] = 405$

$\Leftrightarrow$

$\frac{9}{5} * R^{2} = 405 \Leftrightarrow R^{2} = (\frac{405 * 5}{9}) = 225 \Leftrightarrow R = 15$
Rate = 15%.

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Q:

The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2 years is Rs. 631. Find the sum.

A) 60100	B) 61100
C) 62100	D) 63100

Answer & Explanation Answer: D) 63100

Explanation:

Let the sum be Rs. x. Then,
C.I. = x ( 1 + ( 10 /100 ))^2 - x = 21x / 100 ,
S.I. = (( x * 10 * 2) / 100) = x / 5
(C.I) - (S.I) = ((21x / 100 ) - (x / 5 )) = x / 100
( x / 100 ) = 632 * x = 63100.
Hence, the sum is Rs.63,100.

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Q:

If the compound interest on a certain sum at $16 \frac{2}{3}$ % to 3 years is Rs.1270, find the simple interest on the same sum at the same rate and f or the same period.

A) 1080	B) 1090
C) 1180	D) 1109

Answer & Explanation Answer: A) 1080

Explanation:

Let the sum be Rs. x. Then,

$C . I = [x * {(\frac{50}{300 * 100})}^{3} - x] = (\frac{343 x}{216} - x) = \frac{127 x}{216}$

$\Leftrightarrow \frac{127 x}{216} = 1270$

$x = 2160$

Thus, the sum is Rs. 2160

$S . I = R s . [2160 * \frac{50}{3} * 3 * \frac{1}{100}] = R s 1080$

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Q:

In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?

A) 1years	B) 2years
C) 3years	D) 4years

Answer & Explanation Answer: C) 3years

Explanation:

Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years

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Q:

If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, find the compound interest on the same sum for the same period at the same rate.

A) 1261	B) 1271
C) 1281	D) 1291

Answer & Explanation Answer: A) 1261

Explanation:

Clearly, Rate = 5% p.a., Time = 3 years, S.I.= Rs. 1200. . .
So principal=RS [100*1200]/3*5=RS 8000
Amount = Rs. 8000 x [1 +5/100]^3 - = Rs. 9261.
.. C.I. = Rs. (9261 - 8000) = Rs. 1261.

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