Olympiad Test: Compound Interest - Class 7 MCQ

Amount  = Rs [7500 × (1 + 4/100)²]
= Rs (7500 × 26/25 × 26/25)
= Rs 8112
C.I. = Rs (8112 – 7500)
= Rs 612

Principal = Rs 16, 000;
Time = 9 months = 3 quarters;
Amount = Rs [16000 × (1+5/100)³]
= [16000 × 21/20 × 21/20 × 21/20]
= Rs 18522
C.I = Rs (18522 – 16000)
= Rs 2522

C.I. = Rs [4000 × (1+10/100)² – 4000]
= Rs (4000 × 11/10 × 11/10 – 4000)
= Rs 840
Sum = Rs [420 × 100 /3 × 8] = Rs 1750

Amount  = Rs [8000 × (1+5/100)²]
= Rs [8000 × 21/20 × 21/20]
= Rs 8820

Present worth = Rs [169/(1+4/100)²]
= Rs (169 × 25/26 × 25/26)
= Rs 156.25

Difference in C.I and S.I for 2 years
= Rs (6 96.30 – 660)
= Rs 36.30
S.I for one year =Rs 330
S.I on Rs 330 for 1 year = Rs 36.30
Rate = (100 × 36.30/330 × 1)% = 11% 

S.I = Rs  (1200 × 10 × 1/100)
= Rs 1 20
C.I = Rs  [1200 × (1+5/100)² – 1200]
= Rs 123
Difference = Rs [123 – 120] = Rs 3 

S.I. on Rs 800 for 1 year = Rs [840 – 800]
= Rs 40
Rate = (100 × 40/800 × 1)%
= 5%

Sum = Rs (50 × 100/2×5)
= Rs 500
Amount = [Rs (500 × (1 + 5/100)²]
= Rs (500 × 21/20 × 21/20)
= Rs 551.25
C.I = Rs (551.25 – 500)
= Rs 51.25

Principal = Rs 1000
Amount = Rs 1331
Rate = Rs 10% p.a.
Let the time be n years. Then


Therefore n =  3 years.

Clearly, Rate = 5% p.a.
Time = 3 years
S.I = Rs 1200.
So, Principal = Rs (100 × 1200/3× 5)
= Rs 8000
Amount = Rs [8000 × (1+ 5/100)³]
= Rs (8000 × 21/20 × 21/20 × 21/20)
= Rs 9261
C.I = Rs (9261 – 8000)
= Rs 1261

Amount = Rs (25000 × (1+12/100)³
= Rs (25000 × 28/25 × 28/25 × 28/25)
= Rs 35123.20.
C.I = Rs (35123.20 – 25000)
= Rs 10123.20

Amount = Rs (30000 + 4347)
= Rs 34347
Let the time be n years.
Then, 30000(1+7/100)ⁿ = 34347
⇒ (1+7/100)ⁿ  = 34347/3000
⇒ (107/100)ⁿ = 11449/1000
⇒(107/100)ⁿ = (107/100)²
Therefore  = 2 years

[15000 (1+ r/100)² – 15000] – (15000 × r × 2)/100 = 96
By solving the above equation
r² = (96 × 2)/3  = 64
Therefore r =  8%

Let the sum be Rs P.
Then, [P (1 + 10/100)² – P] = 525
P = (11/10)² – 1 = 525
P = (525 × 100)/21 = 2500
Therefore, sum = Rs 2500
S.I. = (2500 × 5 × 4)/100 = Rs 500

Let the rate be r% p.a.
Then, 1200 × (1 + R/100)² =1348.32
(1 + R/100)² = 11236/10000
(1 + R/100)² = (106/100)²
Therefore r = 6%

P(1 + 20/100)ⁿ > 2P (6/5)ⁿ > 2
Now, (6/5 × 6/5 × 6/5 × 6/5) > 2
So, n = 4 years

Amount of Rs 100 for 1 year when compounded half-yearly
= Rs [100 × (1 + 3/100)²]
= Rs 106.09
Effective rate = (106.09 – 100)% = 6.09%

Let P = Rs 100. Then, S.I. Rs 60 and
T = 6 years.
∴ R = 100 × 60 / 100 × 6 = 10% p.a.
Now, P = Rs 12000 T = 3 years and
R = 10% p.a.
∴ C.I.  = Rs [12000 × (1 +10/100)³ – 1]
= 3972

Amount = [Rs1600 × (1 + 5/2 ×100)² +Rs 1600 × (1 +5/2 ×100)]
= Rs 3321
∴ C.I.= Rs (3321 – 3200) = Rs 121