Aptitude :: Simple And Compound InterestPage 3
17.  A bank offers 5% compound interest calculated on halfyearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:  (a)Rs. 120  (b)Rs. 121  (c)Rs. 122  (d)Rs. 123 

Answer is: BAmount = Rs.[1600 x (1 + 5/2x100) ² + 1600 x (1 + 5/1x100)
= Rs.[1600 x 41/40 x 41/40 + 1600 x 41/40]
= Rs.[1600 x 41/40(41/40 + 1)]
= Rs. [(1600 x 41 x 81)/(40 x 40)]
= Rs. 3321
C.I. = Rs. (3321  3200) = Rs. 121
18.  Divide Rs. 2379 into 3 parts so that their amounts after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is :  (a)759  (b)792  (c)818  (d)828 

Answer is: DLet the parts be X, Y and [2379  (X + Y)]
X + (X x 2 x 5/100) = Y + (Y x 3 x 5/100) = Z + (Z x 4 x 5/100)
11X/10 = 23Y/20 = 6Z/5 = k
X = 10k/11
Y = 20k/23
Z = 5k/6
But X + Y + Z = 2379
1380k + 1320k + 1256k = 2379 x 11 x 23 x 6
k = (2379 x 11 x 23 x 6)/3965 = 910.8
âˆ´ X = (10/11)X910.8 = 828.
19.  Find the compound interest on Rs. 16000 at 20% par annum for 9 months compounded quarterly ?  (a)2252  (b)2522  (c)2344  (d)2122 

Answer is: BP = 16000
N = 9 months = 3 quarters
R = 20% = 5% per quarter.
Amount = [16000 Ã— (1 + 5/100)Â³]
= [16000 Ã— 21/20 Ã— 21/20 Ã— 21/20]
A = 18522
C.I. = 18522  16000 = 2522
20.  In what time will Rs.1000 become Rs.1331 at 10% par annum compounded annually ?  (a)3 years  (b)4 years  (c)5 years  (d)6 years 

Answer is: AP = 1000
A = 1331
R = 10% p.a.
Let the time be n years. Then,
[1000(1+10/100)]â¿ = 1331
(11/10)â¿ = 1331/1000
(11/10)â¿ = (11/10)Â³
n = 3 years.
21.  The difference between the compound interest and the simple interest accured on an amount of Rs.18000 in 2 years was Rs. 405. What was the rate of interest p.c.p.a. ?  (a)10%  (b)15%  (c)18%  (d)20% 

Answer is: BLet the rate be R% p.a. Then,
[18000(1 + R/100)Â²  18000]  (18000 x R x 2)/100 = 405
18000(100 + RÂ²)/1000  1  2R/100] = 405
18000 Ã— [(100 + R)Â²  10000  200R]/10000 = 405
9RÂ²/5 = 405
R = 15%.
22.  A sum of money amounts to Rs.6690 after 3 years and to Rs.10035 after 6 years on compound interest. Find the sum ?  (a)4200  (b)4400  (c)4450  (d)4460 

Answer is: DP(1 + R/100)Â³ = 6690 â€¦â€¦.(i)
P(1 + R/100)^6 = 10035 (note: ^6 is power 6) â€¦â€¦â€¦(ii)
On dividing, we get
(1 + R/100)Â³ = 10035/6690 = 3/2
Putting this value in (i)
P x 3/2 = 6690
P = 4460.
23.  Mohan invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will albert get on maturity of the fixed deposit ?  (a)8600  (b)8820  (c)8800  (d)8840 

Answer is: BAmount = Rs. [8000X(1+5/100)Â²]
= Rs. (8000X21/20X21/20)
= Rs. 8820
24.  Shyam invested Rs. 15000 at the rate of 10% par annum for one year. If the interest is compounded half yearly, then the amount received by Shyam at the end of the year will be ?  (a)16500  (b)16525.50  (c)16537.50  (d)18150 

Answer is: CP = Rs.15000
R =10% p.a. = 5% per halfyear
T = 1 year = 2 halfyears.
âˆ´ Amount = Rs.[15000 x (1+5/100)Â²]
= Rs. (15000 x 21/20 x 21/20)
= Rs. 16537.50.
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