Simple and Compound Interest Questions with Solution (Advanced)

Solution:

Option C

Let the principal amount be ₹P.

CI for 2 years

CI = P(1+20/100)² – P

CI = 44% pf P

SI for 2 years

SI = P * ((30*2)/100)

SI = 60% of P

Given Difference = ₹896

SI - CI = 60% of ₹P - 44% of ₹P

P = ₹896 / 0.16

P = ₹5600

Solution:

Option A

Given, CI - SI = Rs. 1.00

We know, CI - SI for 2 years = P × (R/100)²

1 = P × (4/100)²

1 = P × 0.0016

P = 625

Solution:

Option B

P × [(20/100)³ + 3 × (20/100)²] = 800

P × (16/125) = 800

P = 6250

Solution:

Option D

Using the given data to find the rate of interest (R):

2000 = 150000*R*1/100

2,000 = 1,500 × R

R = 4/3 %

Now, we need to find the principal amount (P_new) to get an interest of  ₹4,500:

Interest (I_new) = ₹4,500

P_new = 4,500 × 75

P_new = 3,37,500

Solution:

Option C

Let the amount borrowed be ₹P.

Interest paid by lender:

SI = P × 4 × 1 / 100 = 0.04P

Interest received by lender:

Rate for half-year = 6% / 2 = 3%

Amount received: A = P(1+3/100)²

P × 1.0609

Interest received = A - P = P × 1.0609 - P = 0.0609P

Gain = Interest received - Interest paid = 0.0609P - 0.04P = 0.0209P Given, Gain = ₹313.50

P = 313.50 / 0.0209 = ₹15,000

Solution:

Option D

S.I for 1 year = Rs. (290/2) = Rs. 145

Difference between S.I and C.I = Rs. (304.5 – 290)

Rs. 14.5

Rate of interest per annum = (14.5/145) × 100%

10%

Solution:

Option A

CI - SI = P(R/100)²

Rate (R) = 25%/2 due to the compounded half-yearly.

4375 = P (25/200)²

P = 4375 × 64 = 280,000

Solution:

Option D

The effective rate of 20% for 2years is = 20 + 20 + (20 × 20)/100 = 44% So, C.I on 1000 for 2 years is = 1000 × 44/100 = 440

Let the principal invest in S.I be P

Now, according to the question,

(P × 4 × 10)/100 = 440/2

P = 1100/2 = 550

Solution:

Option A

Let the principal be ‘P’.

Simple Interest = (Principal × Rate × Time)/100

500 = (Principal × 10 × 2)/100

Principal = 2500

Compound Interest = Principal [(1 + rate/100)^t – 1]

2500[(1 + 10/100)² – 1]

525

Solution:

Option B

Let the rate of interest be R%.

According to the question,

(8000 × R × 3) ÷ 100 = 3600

R = 15%

Now, the same interest rate would be for compounded 8-monthly = 15 ×  8/12 = 10%

So, the amount would become

8000 × (1 + 10/100)^24/8

10648

Solution:

Option A

SI for 1 year = 11,250 ÷ 3 = Rs 3,750

SI for 2 year = 2 × 3750 = Rs 7500

Difference between CI and SI for 2 year = 7650 - 7500 = Rs 150 This difference between CI and SI was on the SI for the 1st year i.e., Rs  3750

Rate % = 150/3750 * 100 = 4%

Principal = Rs 93,750

Solution:

Option D

Here P = 4500 , T = 8 , R = 8%

Simple interest = (P × R × T)/100, where P is the principal, R is the rate of  interest and T is the time period.

Compound interest = [P (1 + R/100)ⁿ] - P, where P is the principal, R is the  rate of interest and n is the time period.

SI = (4500 × 8 × 3)/100 = Rs. 1080

CI = [4500 (1 + 8/100)³] - 4500 = Rs. 5668.7 - 4500 = 1168.7 Required difference = Rs. 88.70

Solution:

Option B

3375 = P × (15/100)²

P = 150000

Solution:

Option A

Amount on S.I = 1200 + P

Amount on C.I = (1200 + P) + 60

Amount on C.I = 1260 + P

Amount on C.I = P + C.I

C.I = Amount on C.I – P

C.I = 1260

Solution:

Option B

Difference = P × (R / 100)² Difference = P × (R / 100)² 981 = P × (5 / 100) (5 / 100) P = 981 × 100 × 100 / 25 P = 981 × 400 = 392400.