Aptitude :: Simple And Compound InterestPage 3

17.

A bank offers 5% compound interest calculated on half-yearly 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
∴ 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 × (1 + 5/100)³]
= [16000 × 21/20 × 21/20 × 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)]ⁿ = 1331
(11/10)ⁿ = 1331/1000
(11/10)ⁿ = (11/10)³
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)² - 18000] - (18000 x R x 2)/100 = 405
18000(100 + R²)/1000 - 1 - 2R/100] = 405
18000 × [(100 + R)² - 10000 - 200R]/10000 = 405
9R²/5 = 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)³ = 6690 …….(i)
P(1 + R/100)^6 = 10035 (note: ^6 is power 6) ………(ii)
On dividing, we get
(1 + R/100)³ = 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)²]
= 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 half-year
T = 1 year = 2 half-years.
∴ Amount = Rs.[15000 x (1+5/100)²]
= Rs. (15000 x 21/20 x 21/20)
= Rs. 16537.50.

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