1. A sum of money becomes four times in 20 years at simple interest. Find the rate of interest.
- 15%
- 12%
- 18%
- 9%
- None of these
Then, the sum after 20 years is ‘4P’
∴ Simple interest = 4P – P = 3P
Formula for S.I = (PRT / 100)
∴ 3P= (P × R × 20) / 100
R = (3P × 100) / (20 × P) = 15 %
Answer: A
2. In 4 year, Rs. 6000 amounts to Rs. 8000. In what time at the same rate, will Rs. 525 amounts to Rs. 700?
- 2 years
- 3 years
- 4 years
- 5 years
- None of these
S.I = A – P = 8000 – 6000 =2000; R =?
Formula for S.I = (PRT / 100)
2000 = (6000 × R × 4) / 100
∴ R = 25/3 %
Now, we calculate T , for A = 700; P= 525;
S.I = A – P = 700 – 525 = 175
S.I = (525 × 25 / 3 × T) / 100
175 = (525 × 25 × T) / (100 × T)
Hence, T = 4 years
Answer: C
3. Swathi borrowed some money at the rate of 6% per annum for the first three years, at the rate of 9% per annum for the next five years and at the rate of 13% per annum for the period beyond eight years. If she pays a total interest of Rs.8160 at the end of eleven years, how much money did she borrow?
- Rs.8000
- Rs.12000
- Rs.10000
- Data inadequate
- None of these
Then, according to the question [(P × 6 × 3) / 100] + [(P × 9 × 5) / 100] + [(P × 13 × 3) / 100] = 8160
(18P + 45P + 39P)/100 = 8160
102P / 100 = 8160
∴ P = 8000
Hence, Swathi borrowed Rs. 8000
Answer: A
4. If a certain sum at compound interest becomes double in 5 year, then in how many years, it will be 16 times at the same rate of interest?
- 10 years
- 15 years
- 20 years
- Cannot be determined
- None of these
X becomes 2X in 5 years
2X becomes 4X in 10 years
4X becomes 8X in 15 years
Hence, 8X becomes 16X in 20 years
Answer: C
5. At simple interest, a sum becomes three times in 20 years. Find the time in which the sum will be double at the same rate of interest?
- 8 years
- 10 years
- 12 years
- 14 years
- None of these
∴ S.I = 3P – P = 2P
Formula for S.I = (PRT) / 100
2P = (P × R × 20) / 100
R = 10%
To find Time (T),
∴ S.I = 2P – P = P
P = (P × 10 × T) / 100
Hence, T = 10 yrs.
Answer: B
6. If the difference between the simple interest and compound interest on some amount at 20% pa for 3 years is 48, then what must be the principal amount?
- Rs. 240
- Rs. 375
- Rs. 480
- Rs. 180
- None of these
P = D × 1003 / R2 (300 + R)
P= 48 × 1003 / 202 (300+20)
P = (48×100×100×100) / [400 (320)] P= 375
Answer: B
7. A sum of money invested at compound interest amounts to Rs. 800 in 3 years and Rs.882 in 5 years. What is the rate of interest?
- Â 2.5%
- Â 4%
- Â 5%
- Â 6.6%
- None of these
A= P (1+R/100)T
Hence, P [1 + (R/100)]3 = 800 …..(1)
P [1 + (R/100)]5 = 882 ….(2)
Since, (2)/(1) = P [1 + (R/100)]5 / P [1 + (R/100)]3 = 882/800
[1 + (R/100)]2 = 441/400
[1 + (R/100)] = √(441 / 400) = 21 / 20
∴ R = (1/20) × 100 = 5%
Answer: C
8. Simple interest for the sum of Rs.1500 is Rs.50 in 4 years and Rs.80 in 8 years. Find the rate of SI?
- 0.5%
- 1%
- 1.5%
- 2%
- None of these
According to the question, = [(1500 × R × 8) / 100] – [(1500 × R × 4) / 100] = 80 – 50 (12000R – 6000R) / 100 = 30
6000R / 100 = 30
R = 30/60 = ½ = 0.5%
Answer: A
9. Simple interest on an amount after 24 months at the rate of 2% per quarter is 960. What is the amount?
- 2000
- 5200
- 6000
- 4800
- None of these
Hence, P = (S.I × 100) / (R×T)
P = (960 × 100) / (8×2) = 6000
Answer: C
10. At what rate percent per annum will a sum of money double in 8 years?
- 10%
- 14%
- 12.5%
- Cannot be determined
- None of these
R = (S.I × 100) / (P×T) = (x ×100) / (x × 8) = 12.5%
Answer: C
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