Simple & Compound Interest: Bank Exam Practice Questions

Ans: C

Explanation: Let P be the principal amount and r be the rate of simple interest per annum.
After 2 years, the amount is Rs. 6600, so P + 2Pr = 6600 (1)
After 5 years, the amount is Rs. 7500, so P + 5Pr = 7500 (2)
Subtracting (1) from (2):
(P + 5Pr) – (P + 2Pr) = 7500 – 6600
3Pr = 900
Pr = 300
Substituting Pr = 300 into (1):
P + 2(300) = 6600
P + 600 = 6600
P = 6600 – 600
P = 6000

Ans: B

Explanation: Let the sum lent to Y be ‘y’. The interest from X is (1000 * 4 * 3) / 100 = 120. The total interest from both X and Y is 360. So, the interest from Y is 360 – 120 = 240. Now, we can find the amount lent to Y using the simple interest formula: 240 = (y * 4 * 3) / 100. Solving for y: y = (240 * 100) / (4 * 3) = 2000.

Ans: E

Explanation:
1. Calculate Simple Interest (SI):
SI = (P * R * T) / 100
Where:
P = Principal = Rs. 72000
R = Rate = 9% per annum
T = Time = 5 years
SI = (72000 * 9 * 5) / 100 = Rs. 32400

2. Calculate Compound Interest (CI):
CI = P(1 + R/100)^T – P
Where:
P = Principal = Rs. 56000
R = Rate = 7% per annum
T = Time = 3 years
CI = 56000(1 + 7/100)^3 – 56000
CI = 56000(1.07)^3 – 56000
CI = 56000 * 1.225043 – 56000
CI = 68602.408 – 56000
CI = Rs. 12602.408

3. Calculate the percentage:
Percentage = (CI / SI) * 100
Percentage = (12602.408 / 32400) * 100
Percentage ≈ 38.90%

This calculation results in an answer very close to Option E. However, we’ll choose the closest, more accurate one.
Correct Option: E

Ans: B

Explanation: Let P be the principal (Rs. 46875), R be the rate of interest, and T be the time (3 years). The compound interest (CI) is Rs. 12174. The formula for compound interest is: Amount = P(1 + R/100)^T. Amount = Principal + Compound Interest. So, Amount = 46875 + 12174 = 59049.

Therefore, 59049 = 46875(1 + R/100)^3.
(1 + R/100)^3 = 59049/46875 = 1.2597.
Taking the cube root of both sides: 1 + R/100 = 1.08.
R/100 = 0.08
R = 8%.

Alternatively,
Amount = Principal + Interest
Amount = 46875 + 12174 = 59049
Amount = P(1 + R/100)^T
59049 = 46875(1 + R/100)^3
(1+R/100)^3 = 59049/46875 = 1.2597
Trying the options:
A. 10%: Amount = 46875(1+10/100)^3 = 46875 * 1.1^3 = 46875 * 1.331 = 62300 approx
B. 8%: Amount = 46875(1+8/100)^3 = 46875 * 1.08^3 = 46875 * 1.2597 = 59049
Since the calculated amount is equal to Principal+Interest, the right rate is 8%.

Correct Option: B

Ans: C

Explanation:
Simple Interest:
Principal (P) = Rs. 9000
Rate (R) = 10% per annum
Time (T) = 3 years
Simple Interest (SI) = P * R * T / 100
SI = 9000 * 10 * 3 / 100 = Rs. 2700

Compound Interest:
Principal (P) = Rs. 9000
Rate (R) = 20% per annum
Time (T) = 2 years
Amount (A) = P * (1 + R/100)^T
A = 9000 * (1 + 20/100)^2
A = 9000 * (1.2)^2
A = 9000 * 1.44
A = Rs. 12960
Compound Interest (CI) = A – P
CI = 12960 – 9000 = Rs. 3960

Difference in interest = CI – SI
Difference = 3960 – 2700 = Rs. 1260

Correct Option: C

Ans: D

Explanation:
Let P be the principal amount.
Simple Interest (SI) for 2 years at 10% annual interest rate:
SI = P * R * T / 100 = P * 10 * 2 / 100 = 0.2P

Compound Interest (CI) for 2 years compounded semi-annually:
Interest rate per half-year = 10/2 = 5% = 0.05
Number of compounding periods = 2 * 2 = 4
CI = P(1 + r)^n – P = P(1 + 0.05)^4 – P = P(1.05)^4 – P = P(1.21550625) – P = 0.21550625P

The difference between CI and SI is Rs. 124.05:
CI – SI = 124.05
0.21550625P – 0.2P = 124.05
0.01550625P = 124.05
P = 124.05 / 0.01550625
P = 8000

Correct Option: D

Ans: C

Explanation: Let P be the principal.
Simple Interest (SI) for 2 years at 20%: SI = P * 20/100 * 2 = 0.4P
Compound Interest (CI) for 2 years at 20%: CI = P(1 + 20/100)^2 – P = P(1.2)^2 – P = 1.44P – P = 0.44P
CI – SI = 200 => 0.44P – 0.4P = 200 => 0.04P = 200 => P = 200/0.04 = 5000
Now, for 3 years at 12% simple interest: SI = 5000 * 12/100 * 3 = 5000 * 0.12 * 3 = 1800
Correct Option: C

Ans: A

Explanation: Let P be the principal amount. If the sum triples in 8 years, then after 8 years, the amount becomes 3P. Using the compound interest formula: A = P(1 + r)^n, where A is the amount, P is the principal, r is the rate of interest, and n is the number of years.

After 8 years, 3P = P(1 + r)^8. This simplifies to (1 + r)^8 = 3.

We want to find the time it takes for the amount to become 9 times the principal, which is 9P. So, we need to find n such that 9P = P(1 + r)^n. This simplifies to (1 + r)^n = 9.

Since (1 + r)^8 = 3, we can square both sides to get ((1 + r)^8)^2 = 3^2, which simplifies to (1 + r)^16 = 9.

Therefore, n = 16.

Ans: D

Explanation: Let the principal be P and the original rate of interest be R.
Simple Interest = P * R * T / 100
In the first case, Simple Interest = P * R * 4 / 100
In the second case, the rate is R+3, Simple Interest = P * (R+3) * 4 / 100
The difference in interest is Rs. 1800.
So, P * (R+3) * 4 / 100 – P * R * 4 / 100 = 1800
(4PR + 12P – 4PR) / 100 = 1800
12P / 100 = 1800
P = (1800 * 100) / 12
P = 15000

Ans: C

Explanation: The interest is compounded quarterly, meaning every 3 months. The rate of interest is 12% per annum, so the rate per quarter is 12%/4 = 3%. The principal is Rs. 10000. After 3 months, we are calculating the interest for only one quarter. Compound Interest = P(1+r/100)^n – P = 10000(1+3/100)^1 – 10000 = 10000(1.03) – 10000 = 10300 – 10000 = 300.

Ans: A

Explanation:First, find the initial investment (P) using the compound interest formula: A = P(1 + r/n)^(nt). In this case, A = 3456, r = 0.20, n = 1, and t = 3. So, 3456 = P(1 + 0.20)^3, or 3456 = P(1.2)^3. Therefore, 3456 = P * 1.728. Solving for P, P = 3456 / 1.728 = 2000. Next calculate 3P = 3 * 2000 = 6000. Now, calculate simple interest. Simple Interest = P * r * t, where P is the principal, r is the rate, and t is the time. Simple Interest = 6000 * 0.15 * 12 = 10800.

Correct Option: A

Ans: E

Explanation:
Quantity A: Simple Interest
SI = PRT/100
10800 = (24000 * R * 3)/100
R = (10800 * 100) / (24000 * 3)
R = 15%

Quantity B: Compound Interest
Amount = Principal + Compound Interest
Amount = 16000 + 8334 = 24334
A = P(1+R/100)^T
24334 = 16000(1+R/100)^3
(1+R/100)^3 = 24334/16000 = 1.520875
1 + R/100 = 1.15
R/100 = 0.15
R = 15%

Quantity A = 15%
Quantity B = 15%
Therefore Quantity A = Quantity B.

Correct Option: E

Ans: E

Explanation: Let P be the principal amount borrowed by X and Y.
X’s interest = P * R * T = P * 0.06 * 3 = 0.18P
Y’s interest = P * R * T = P * 0.08 * 3 = 0.24P
Y paid Rs 120 more in interest than X. Therefore,
0.24P – 0.18P = 120
0.06P = 120
P = 120 / 0.06
P = 2000

Ans: D

Explanation: Simple Interest (SI) = P * R * T / 100 = 10000 * 10 * 2 / 100 = Rs. 2000
Compound Interest (CI) = P * [(1 + R/100)^T – 1] = 10000 * [(1 + 10/100)^2 – 1] = 10000 * [(1.1)^2 – 1] = 10000 * [1.21 – 1] = 10000 * 0.21 = Rs. 2100
Difference between CI and SI = 2100 – 2000 = Rs. 100

Ans: C

Explanation: First, calculate the interest for the first 2 years at 12%. Then, calculate the remaining interest for the next 3 years at 20%. Subtract the interest Sumesh would have paid at 12% for the entire 5 years to find the extra interest.

Interest for the first 2 years at 12%:
Simple Interest = P * R * T / 100
Interest = 50000 * 12 * 2 / 100 = Rs. 12,000

Interest for the next 3 years at 20%:
Interest = 50000 * 20 * 3 / 100 = Rs. 30,000

Total Interest Paid = 12,000 + 30,000 = Rs. 42,000

If the interest rate remained at 12% for 5 years:
Interest = 50000 * 12 * 5 / 100 = Rs. 30,000

Extra Interest = 42,000 – 30,000 = Rs. 12,000

Correct Option: C

Ans: A

Explanation: Let P be the amount borrowed. The simple interest for 2 years is P * 8% * 2 = 0.16P. The simple interest for 3 years is P * 8% * 3 = 0.24P. The difference in interest is 0.24P – 0.16P = 0.08P. We are given that this difference is Rs. 96. Therefore, 0.08P = 96. Solving for P, we get P = 96 / 0.08 = 1200.

Correct Option: A