Simple Interest problems
- 1. What annual payment will discharge a debt of ? 1092 due in 2 yr at 12% simple interest?
Options- A. ? 725
- B. ? 325
- C. ? 515
- D. ? 900 Discuss
Correct Answer: ? 515
Explanation:
According to the formula,
Annual payment = 100P / [100 x T + {RT (T - 1)/2}]
= (1092 x 100) / [100 x 2 + {24 (2 - 1)/2}]
= (1092 x 100)/2012
= ? 515.09
? ? 515
- 2. What annual payment will discharge a debt of ? 1696 in yr at 4% per annum?
Options- A. ? 525
- B. ? 425
- C. ? 325
- D. ? 400 Discuss
Correct Answer: ? 400
Explanation:
Given, debt (p) = ? 1696, R = 4% T = 4 yr
According to the formula,
Annual payment = 100P / [100 x T + {RT (T - 1)/2}]
= (1696 x 100) / [4 x 100 + {(4 x 3 x 4)/2}]
= (1696 x 100) / 424
= ? 400
- 3. Harsha makes a fixed deposit of ? 20000 in Bank of India for a period of 3 yr. If the rate of interest be 13% SI per annum charged half - yearly, what amount will he get after 42 months?
Options- A. ? 27800
- B. ? 28100
- C. ? 29100
- D. ? 30000 Discuss
Correct Answer: ? 29100
Explanation:
Give, time = 42 months.
= (42/12) yr = 31/2 yr
= 7 half - yr,
rate = 13/2% half - yearly
SI = (20000 x 13 x 7)/(100 x 2) = ? 9100
? Amount (A) = 20000 + 9100
= ? 29100
- 4. A certain sum at simple interest amount to ? 1350 in 5 yr and to ? 1620 in 8 yr what is the sum?
Options- A. ? 700
- B. ? 800
- C. ? 900
- D. ? 1000 Discuss
Correct Answer: ? 900
Explanation:
Given, A1 = ? 1350, A2 =? 1620
T1 = 5 yr and T2 = 8 yr
Let principal amount be ? P.
? In time = 8 - 5 = 3 yr
Simple interest will be
1620 - 1350 = ? 270
? R = [(A2 - A1 ) x 100] / [A1 T2 - A2 T1]
= [(1620 - 1350) x 100] / [(1350 x 8) - (1620 X 5)]
= (270 x 100)/[10800 - 8100]
= 27000/2700
? R = 10%
? P = (SI x 100) / (R x T)
= (270 x 100) / (10 x 3)
= ? 900
- 5. In 4 yr. ? 6000 amounts to ? 8000. In what time at the same rate, will ? 525 amount to ? 700?
Options- A. 2 yr
- B. 3 yr
- C. 4 yr
- D. 5 yr Discuss
Correct Answer: 4 yr
Explanation:
Amount = ? 8000
Time (T) = 4 yr; Principal (P) = ? 6000
Simple interest (SI) = (A - P)
= Amount - Principal
= 8000 - 6000 = ? 2000
Rate (R) = ?
According to the formula. SI = (P x R x T)/100
? 2000 = (6000 x R x 4)
? R = (6000 x 100)/(6000 x 4) = (25/3) %
Now, again Amount (A) = ? 700
Principle (P) = ? 525, Time (T) = ?
Rate (R) = 25/3%
Simple interest = A - P
? 700 - 525 = ? 175
Using formula, SI = (P x R x T) / 100
? 175 = [525 x (25/3) x T] / 100
? T = (175 x 100 x 3) / (525 x 25)
= 4 yr
- 6. A Principal amounts to ? 944 in 3 yr and to ? 1040 in 5 yr, each sum being invested at the same simple interest. The principal was
Options- A. ? 800
- B. ? 991
- C. ? 750
- D. ? 900 Discuss
Correct Answer: ? 800
Explanation:
By formula, P = (A2T1 - A1T2) / (T1 - T2)
Here, A1 = ? 944, T1 = 3
A2 = ? 1040, T2 = 5
? P = [(1040 x 3) - (944 x 5)] / (3 - 5)
= (3120 - 4720) / (-2)
= (-1600) / (-2)
= ? 800
? Principal = ? 800
- 7. A sum of ? 1550 was lent partly at 5% and partly at 8% per annum simple interest. The total interest received after 4 yr was ? 400, The ratio of the money lent at 5% to that lent at 8% is
Options- A. 16 : 15
- B. 17 : 15
- C. 16 : 13
- D. 16 : 19 Discuss
Correct Answer: 16 : 15
Explanation:
Let the sum lent at 5% = P
? Sum lent at 8% = (1550 - P)
Then, [(P x 5 x 4)/100] + [{(1550 - P) x 8 x 4}/100] = 400
? 20P - 32P + 1550 x 32 = 40000
? - 12P + 49600 = 40000
? - 12P = - 9600
? p = ? 800
Sum lent at 8% = 1550 - 800 = ? 750
? Required ratio = 800 : 750 = 16 : 15
- 8. Neeta borrowed some money at the rate of 6% per annum for the first 3 yr. at the rate of 9% per annum for the next 5 yr and a the rate of 13% per annum for the period beyond 8 yr. If she pays a total interest of ? 8160 at the and of 11 yr how much money did she borrow?
Options- A. ? 12000
- B. ? 10000
- C. ? 8000
- D. Data is inadequate Discuss
Correct Answer: ? 8000
Explanation:
Let the sum borrowed = P
Then, according to the question,
[(P x 6 x 3)/100] + [(P x 9 x 5)/100] + [(P x 13 x 3)/100] = 8160
? (18P + 45P +39P) / 100 = 8160
? 102P/100 = 8160
? P = (8160 x 100)/102
? P = ? 8000
- 9. Reena had ? 10000 with her, out of this money she lent some money to Akshay for 2 yr at 15% simple interest. She lent remaining money to Brijesh for an equal number of years at the rate of 18%. After 2 yr Reena found that Akshay had given her 360 more as interest as compared to Brijesh. The amount of money which Reena had lent to Brijesh must be
Options- A. ? 4000
- B. ? 2500
- C. ? 3500
- D. ? 4200 Discuss
Correct Answer: ? 4000
Explanation:
Let the money lent to Akshay = ? P
Then, money lent to Brijesh = ? (10000 - P) [as total amount = ? 10000]
SI for Akshay = (P x 15 x 2)/100 = 3P/10
SI for Brijesh = {(10000 - P) x 18 x 2}/100 = 9/25 (10000 - P)
According to the given condition, (3P/10) - [(9/25) x ( 10000 - P ) = 360
[as SI (Akshay) - SI (Brijesh) = 360]
? (3P/10) - 3600 + 9P/25 = 360
? 3P/10 + 9P/25 = 360 + 3600 = 3960
? 33P/50 = 3960
? P = 3960 x 50/33
? P = 6000
? The amount of money lent to Brijesh
= 10000 - 6000 ? 4000
- 10. Mr. Pawan invests an amount of ? 242000 at the rate of 4% per annum for 6 yr to obtain a simple interest, later he invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same rate of interest. What amount of simple interest will be obtained at the end of the last 4 yr?
Options- A. ? 4800
- B. ? 4850.32
- C. ? 4801.28
- D. ? 4700 Discuss
Correct Answer: ? 4801.28
Explanation:
In the case I,
SI = (P x R x T) /100 = (24200 x 4 x 6) / 100 = ? 5808
? Amount = Principal + SI
SI = 24200 + 5808 = 30008
In the case II,
SI = (30008 x 4 x 4) / 100 = ? 4801.28
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