📘 Quiz

Test your skills & challenge yourself 🚀

Question 1 / 20
1:00
1
An individual lends Rs. 11000 to a friend, to be repaid in 3 annual installments with a 20% annual compound interest rate. Calculate the amount of each installment.
0:00
Solution: Step 1: Let each installment = x Step 2: Present value of annuity formula: 11000 = x / (1 + 0.20) + x / (1 + 0.20)^2 + x / (1 + 0.20)^3 Step 3: Calculate present values: x / 1.20 + x / 1.44 + x / 1.728 = 11000 Step 4: Multiply through by 1.728 to clear denominators: 1.44x + 1.2x + x = 11000 * 1.728 Step 5: Combine like terms: 3.64x = 19008 Step 6: Solve for x: x = 19008 / 3.64 = 5221.97 Step 7: Each installment = Rs. 5221.97
2
An individual's earnings double annually, starting from an initial amount of Rs. 4 lakhs. What will be the total earnings after 6 years?
0:00
Solution: Step 1: Initial earnings = Rs. 4 lakhs Step 2: After 1 year = 4 * 2^1 = Rs. 8 lakhs Step 3: After 2 years = 4 * 2^2 = Rs. 16 lakhs Step 4: After 6 years = 4 * 2^6 = 4 * 64 = Rs. 256 lakhs Step 5: Convert to crores = 256 lakhs = Rs. 2.56 crores
3
A specific sum of money, compounded annually at an R% interest rate, grows to Rs. 1440 after two years and Rs. 1728 after three years. What is the value of R%?
0:00
Solution: Step 1: For compound interest, the amount at the end of the (n-1)th year serves as the principal for the nth year. Step 2: The amount after 2 years is Rs. 1440. Step 3: The amount after 3 years is Rs. 1728. Step 4: The interest earned in the 3rd year (from the end of year 2 to the end of year 3) is: Interest = Rs. 1728 - Rs. 1440 = Rs. 288. Step 5: This interest of Rs. 288 is earned on the principal of Rs. 1440 over 1 year. Step 6: Calculate the annual interest rate (R%): R = (Interest / Principal) * 100 R = (288 / 1440) * 100 = (1/5) * 100 = 20%.
4
If the compound interest earned on Rs. 30,000 at 7% per annum is Rs. 4347, what is the duration of the investment in years?
0:00
Solution: Step 1: Given Principal (P) = Rs. 30,000, Compound Interest (CI) = Rs. 4347, and Rate (R) = 7% per annum. Step 2: Calculate the total Amount (A) = P + CI = 30000 + 4347 = Rs. 34347. Step 3: Use the compound interest formula: A = P * (1 + R/100)^n, where n is the time in years. Step 4: Substitute the known values: 34347 = 30000 * (1 + 7/100)^n. Step 5: 34347 / 30000 = (107/100)^n. Step 6: Simplify the fraction on the left side: Divide both numerator and denominator by 3. 34347 / 3 = 11449. 30000 / 3 = 10000. Step 7: So, 11449 / 10000 = (107/100)^n. Step 8: Recognize that 11449 is 107 squared (107 * 107) and 10000 is 100 squared (100 * 100). Step 9: Therefore, (107/100)^2 = (107/100)^n. Step 10: By comparing the exponents, n = 2 years.
5
A principal amount grows to Rs. 900 in 3 years and Rs. 1000 in 4 years under compound interest. Determine the principal and the annual interest rate.
0:00
Solution: Step 1: Let Principal = P, Rate = R% Step 2: After 3 years: P * (1 + R/100)^3 = 900 Step 3: After 4 years: P * (1 + R/100)^4 = 1000 Step 4: Divide equation (3) by (2): (1 + R/100) = 1000/900 Step 5: (1 + R/100) = 10/9 => R/100 = 1/9 => R = 11.11% Step 6: Substitute R back into equation (2): P * (1 + 11.11/100)^3 = 900 Step 7: P * (1.111)^3 = 900 Step 8: P * 1.367 = 900 => P = 900 / 1.367 = Rs. 658.30 (approx Rs. 656.10)
6
A building valued at Rs. 133100 is built on land worth Rs. 72900. How many years will it take for their values to become equal, given that the land appreciates by 10% annually and the building depreciates by 10% annually?
0:00
Solution: Step 1: Let the initial value of land (L0) = Rs. 72900 and the initial value of the building (B0) = Rs. 133100. Step 2: Let the annual appreciation rate for land (rL) = 10% and the annual depreciation rate for building (rB) = 10%. Step 3: The value of land after 'n' years will be L(n) = L0 * (1 + rL)^n = 72900 * (1.1)^n. Step 4: The value of the building after 'n' years will be B(n) = B0 * (1 - rB)^n = 133100 * (0.9)^n. Step 5: To find when their values are the same, set L(n) = B(n). 72900 * (1.1)^n = 133100 * (0.9)^n Step 6: Rearrange the equation: (1.1)^n / (0.9)^n = 133100 / 72900 (11/10)^n / (9/10)^n = 1331 / 729 (11/9)^n = 1331 / 729 Step 7: Recognize that 1331 = 11^3 and 729 = 9^3. (11/9)^n = (11/9)^3 Step 8: By comparing the exponents, n = 3 years.
7
A principal amount, when compounded annually, grows to Rs. 11,880 after 4 years and to Rs. 17,820 after 6 years. Determine half of the original principal sum.
0:00
Solution: Step 1: Use the given amounts at different times to find the growth factor. Let P be the principal and (1 + R/100) be the annual growth factor 'k'. Amount after 4 years (A4) = P * k^4 = Rs. 11,880 (Equation 1) Amount after 6 years (A6) = P * k^6 = Rs. 17,820 (Equation 2) Divide Equation 2 by Equation 1: (P * k^6) / (P * k^4) = 17820 / 11880 k^2 = 1.5 So, k^2 = 3/2. Step 2: Use the growth factor to find the principal (P). From Equation 1: P * k^4 = 11880 We can write k^4 as (k^2)^2. P * (3/2)^2 = 11880 P * (9/4) = 11880 P = (11880 * 4) / 9 P = 1320 * 4 P = Rs. 5,280. Step 3: Calculate half of the principal sum. Half of the sum = P / 2 = 5280 / 2 = Rs. 2,640.
8
A sum of money is invested at 20% compound interest per annum for 2 years, yielding Rs.96.4 more when interest is compounded half-yearly instead of annually. What is the principal amount?
0:00
Solution: Step 1: Let the principal amount = P Step 2: Annual compounding interest for 2 years = P * (1 + 0.20)^2 - P Step 3: Half-yearly compounding interest for 2 years = P * (1 + 0.10)^4 - P Step 4: Difference in interest = Half-yearly interest - Annual interest = 96.4 Step 5: Set up equation: P * (1.10)^4 - P - [P * (1.20)^2 - P] = 96.4 Step 6: Simplify: P * (1.4641 - 1.44) = 96.4 Step 7: Solve for P: P * 0.0241 = 96.4 Step 8: P = 96.4 / 0.0241 = 4000 Principal amount = Rs. 4000
9
Determine the initial investment amount if the difference between the compound interest and simple interest earned over 3 years at an annual rate of 25% is Rs. 320.
0:00
Solution: Step 1: Let the principal amount = P Step 2: Simple Interest (SI) = P * R * T / 100 = P * 25 * 3 / 100 = 0.75P Step 3: Compound Interest (CI) = P * (1 + R/100)^T - P = P * (1 + 25/100)^3 - P = P * (1.25)^3 - P = P * 1.953125 - P = 0.953125P Step 4: Difference between CI and SI = 0.953125P - 0.75P = 0.203125P Step 5: Given difference = Rs. 320, so 0.203125P = 320 Step 6: Solve for P: P = 320 / 0.203125 = 1575.38 Step 7: Principal amount = Rs. 1575.38
10
A bank provides a 5% compound interest rate, with interest calculated every half-year. A customer makes two deposits: Rs. 1600 on January 1st and another Rs. 1600 on July 1st of the same year. How much interest would the customer have earned by the year's end?
0:00
Solution: Step 1: The annual interest rate is 5%, and it's compounded half-yearly. Therefore, the interest rate per half-year (i) = 5% / 2 = 2.5%. Step 2: Calculate the amount for the first deposit of Rs. 1600 made on January 1st. This deposit earns interest for two half-year periods (1 year). Amount1 = P * (1 + i/100)^n = 1600 * (1 + 2.5/100)^2 = 1600 * (1 + 1/40)^2 = 1600 * (41/40)^2 = 1600 * (1681 / 1600) = Rs. 1681. Step 3: Calculate the amount for the second deposit of Rs. 1600 made on July 1st. This deposit earns interest for one half-year period (from July to December). Amount2 = P * (1 + i/100)^n = 1600 * (1 + 2.5/100)^1 = 1600 * (41/40) = Rs. 1640. Step 4: Calculate the total amount at the end of the year = Amount1 + Amount2 = 1681 + 1640 = Rs. 3321. Step 5: Calculate the total principal deposited = 1600 + 1600 = Rs. 3200. Step 6: The total interest gained by the customer = Total Amount - Total Principal = 3321 - 3200 = Rs. 121. Step 7: The interest gained is Rs. 121.
11
A loan is to be repaid in two identical annual installments of Rs. 44,100 each. Given an annual compound interest rate of 5%, what is the total interest paid on this loan?
0:00
Solution: Step 1: Understand the formula for present value of installments. The present value (Principal) of an installment (I) paid after 'n' years at 'R' rate is P = I / (1 + R/100)^n. Given: Each installment (I) = Rs. 44,100, Rate (R) = 5% p.a. Step 2: Calculate the present value of the first installment. P1 = 44100 / (1 + 5/100)^1 = 44100 / 1.05 = Rs. 42,000. Step 3: Calculate the present value of the second installment. P2 = 44100 / (1 + 5/100)^2 = 44100 / (1.05)^2 = 44100 / 1.1025 = Rs. 40,000. Step 4: Calculate the total principal (sum borrowed). Total Principal = P1 + P2 = 42000 + 40000 = Rs. 82,000. Step 5: Calculate the total amount paid. Total Amount Paid = 2 * I = 2 * 44100 = Rs. 88,200. Step 6: Calculate the total interest paid. Total Interest = Total Amount Paid - Total Principal Total Interest = 88200 - 82000 = Rs. 6,200.
12
Determine the annual compound interest rate at which an initial sum of Rs. 1200 will grow to Rs. 1348.32 over a period of 2 years.
0:00
Solution: Step 1: Identify given values: Principal (P) = Rs. 1200, Amount (A) = Rs. 1348.32, Time (n) = 2 years. Step 2: Recall the compound interest formula: A = P(1 + R/100)^n. Step 3: Substitute the values into the formula: 1348.32 = 1200(1 + R/100)^2. Step 4: Divide both sides by 1200: 1348.32 / 1200 = (1 + R/100)^2. Step 5: Simplify the fraction: 1.1236 = (1 + R/100)^2. Step 6: Take the square root of both sides: sqrt(1.1236) = 1 + R/100. Step 7: Calculate the square root: 1.06 = 1 + R/100. Step 8: Subtract 1 from both sides: 0.06 = R/100. Step 9: Multiply by 100 to find R: R = 0.06 * 100 = 6%. Step 10: The annual compound interest rate is 6%.
13
The difference between the compound interest and simple interest accrued on an amount of Rs. 26000 at the end of 3 years is Rs. 2994.134. What is the annual rate of interest?
0:00
Solution: Step 1: Let the principal be P = Rs. 26000, time T = 3 years, and the annual rate of interest be R%. Step 2: Use the formula for the difference between CI and SI for 3 years: Difference = P * (R/100)^2 * (3 + R/100). Step 3: Substitute the given values: 2994.134 = 26000 * (R/100)^2 * (3 + R/100). Step 4: Rearrange the equation: 2994.134 / 26000 = (R^2 / 10000) * ((300 + R) / 100). Step 5: Simplify: 0.115159 = (R^2 * (300 + R)) / 1000000. Step 6: Multiply both sides by 1000000: 115159 = R^2 * (300 + R). Step 7: Now, we need to find an integer value of R that satisfies this equation. We can test values or look for factors. Step 8: Try common interest rates: - If R = 10%, R^2 * (300+R) = 100 * 310 = 31000 (too low). - If R = 15%, R^2 * (300+R) = 225 * 315 = 70875 (too low). - If R = 18%, R^2 * (300+R) = 324 * 318 = 103032 (close). - If R = 19%, R^2 * (300+R) = 361 * 319 = 115159 (Exact Match!). Step 9: Therefore, the annual rate of interest (R) is 19%.
14
A certain sum of money, when invested at an 8% annual compound interest rate, accumulates to Rs. 5832 in 2 years. Determine the original sum.
0:00
Solution: Step 1: Given Amount (A) = Rs. 5832. Step 2: Given Time (T) = 2 years. Step 3: Given Rate (R) = 8% p.a. Step 4: Use the compound interest amount formula: A = P * (1 + R/100)^T. Step 5: 5832 = P * (1 + 8/100)^2. Step 6: 5832 = P * (1.08)^2. Step 7: 5832 = P * 1.1664. Step 8: P = 5832 / 1.1664 = Rs. 5000.
15
A principal sum of Rs. 10,500 grows to Rs. 13,650 over 2 years at a certain simple interest rate per annum. What will be the total amount if the same sum is invested for 1 year at the same rate, but with interest compounded half-yearly? (Round to the nearest rupee)
0:00
Solution: Step 1: Calculate the simple interest rate (R). Principal (P) = Rs. 10,500 Amount (A) = Rs. 13,650 Time (T) = 2 years Simple Interest (SI) = A - P = 13650 - 10500 = Rs. 3,150. Formula: SI = (P * R * T) / 100 3150 = (10500 * R * 2) / 100 3150 = 210 * R R = 3150 / 210 = 15% per annum. Step 2: Calculate the amount if the same sum is compounded half-yearly for 1 year at the rate found in Step 1. Principal (P') = Rs. 10,500 Annual Rate (R) = 15% p.a. Time (T') = 1 year For half-yearly compounding: Rate per period = R/2 = 15%/2 = 7.5% Number of periods = T' * 2 = 1 * 2 = 2 periods Formula for Amount (A_CI) = P' * (1 + (Rate per period)/100)^(Number of periods) A_CI = 10500 * (1 + 7.5/100)^2 A_CI = 10500 * (1.075)^2 A_CI = 10500 * 1.155625 A_CI = 12134.0625 Step 3: Round the amount to the nearest rupee. A_CI = Rs. 12,134.
16
A loan is repaid through two identical annual instalments of Rs. 5,808 each. If the annual compound interest rate is 10%, what is 60% of the total interest (rounded to the nearest Rupee) charged in this repayment scheme?
0:00
Solution: Step 1: Identify given values: Instalment (x) = Rs. 5808, Rate (R) = 10% p.a., Time = 2 years. Step 2: Calculate the present value (principal) of the loan. Principal (P) = x / (1 + R/100)^1 + x / (1 + R/100)^2 P = 5808 / (1 + 10/100)^1 + 5808 / (1 + 10/100)^2 P = 5808 / (11/10) + 5808 / (121/100) P = (5808 * 10 / 11) + (5808 * 100 / 121) P = 5280 + 4800 = Rs. 10080. Step 3: Calculate the total amount paid in instalments. Total amount paid = 2 * Instalment = 2 * 5808 = Rs. 11616. Step 4: Calculate the total interest charged. Total Interest = Total Amount Paid - Principal = 11616 - 10080 = Rs. 1536. Step 5: Calculate 60% of the total interest. 60% of Total Interest = 0.60 * 1536 = Rs. 921.6. Step 6: Round to the nearest Rupee: Rs. 922. Step 7: 60% of the total interest charged is Rs. 922.
17
A mobile phone costs Rs. 25,000. It can be purchased with a Rs. 5,000 down payment, followed by 3 equal annual installments at a 25% p.a. compound interest rate. What is the value of each installment, rounded to two decimal places?
0:00
Solution: Step 1: Calculate the principal amount that needs to be financed through installments. Total cost of mobile phone = Rs. 25,000. Down payment = Rs. 5,000. Amount to be financed (Principal P) = Total cost - Down payment = 25000 - 5000 = Rs. 20,000. Step 2: Identify the interest rate and number of installments. Annual compound interest rate (R) = 25%. Number of equal annual installments (n) = 3. Step 3: Set up the formula for equal annual installments. Let 'x' be the amount of each installment. The present value (P) of the loan is the sum of the present values of all future installments. P = x / (1 + R/100)^1 + x / (1 + R/100)^2 + x / (1 + R/100)^3 Step 4: Substitute values and solve for 'x'. Since R = 25% = 1/4, then (1 + R/100) = (1 + 1/4) = 5/4. 20000 = x / (5/4) + x / (5/4)^2 + x / (5/4)^3 20000 = x * (4/5) + x * (16/25) + x * (64/125) 20000 = x * ( (4*25)/125 + (16*5)/125 + 64/125 ) 20000 = x * (100/125 + 80/125 + 64/125) 20000 = x * ( (100 + 80 + 64) / 125 ) 20000 = x * (244 / 125) x = (20000 * 125) / 244 x = 2500000 / 244 x = 10245.9016... Step 5: Round the value of each installment to two decimal places. Each installment = Rs. 10,245.90.
18
Determine the difference between the simple interest and compound interest accumulated on a principal of Rs. 2000 at an annual rate of 5% over 2 years.
0:00
Solution: Step 1: Identify the given values: Principal (P) = Rs. 2000, Rate (R) = 5% per annum, Time (n) = 2 years. Step 2: Use the direct formula for the difference between CI and SI for 2 years: Difference = P × (R/100)^2. Step 3: Substitute the values into the formula: Difference = 2000 × (5/100)^2. Step 4: Calculate the difference: Difference = 2000 × (1/20)^2 = 2000 × (1/400). Step 5: Simplify: Difference = 2000 / 400 = Rs. 5.
19
An individual invested Rs. 20,000 at an annual interest rate of 8%, compounded semi-annually. What is the total interest earned at the end of the year?
0:00
Solution: Step 1: Principal (P) = Rs. 20,000 Step 2: Annual interest rate = 8%, Semi-annual rate = 8/2 = 4% Step 3: Time = 1 year, compounded semi-annually = 2 periods Step 4: Amount = P * [1 + (rate/100)]^time = 20000 * [1 + (4/100)]^2 Step 5: Amount = 20000 * [1 + 0.04]^2 = 20000 * (1.04)^2 Step 6: Amount = 20000 * 1.0816 = Rs. 21632 Step 7: Total compound interest = Amount - Principal = 21632 - 20000 = Rs. 1632
20
An investor allocated funds into two investment plans, Plan X offering 8% annual compound interest and Plan Y offering 9% annual compound interest. After two years, the combined interest from both plans totaled Rs. 5,527.30, with a total investment of Rs. 31,000. What amount was invested in Plan X?
0:00
Solution: Step 1: Let amount in Plan X = A, amount in Plan Y = B Step 2: A + B = 31000 (Total investment) Step 3: Interest from Plan X = A * (1.08)^2 - A Step 4: Interest from Plan Y = B * (1.09)^2 - B Step 5: Total interest = 5527.30 Step 6: Set up equation: [A * (1.08)^2 - A] + [B * (1.09)^2 - B] = 5527.30 Step 7: Substitute B = 31000 - A into equation Step 8: Solve for A, yielding A = 14000
📊 Questions Status
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20