Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice

Rachna borrows Rs. 12,000 at 10 per cent annum interest compound half-yearly. She repays Rs. 4,000 at the end of every six months. Calculate the third payment she has to make at the end of 18 month in order to clear the entire loan.

  1. Rs. 5281.50

  2. Rs. 2,678.9

  3. Rs. 2,345.6

  4. Rs. 2,098.7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal 12000, rate 10% per annum (5% per half-year). Period 1: 12000 * 1.05 - 4000 = 12600 - 4000 = 8600. Period 2: 8600 * 1.05 - 4000 = 9030 - 4000 = 5030. Period 3: 5030 * 1.05 = 5281.50.

Multiple choice

The compound interest on a sum for $2$ years is Rs. $832$ and the simple interest on the same sum for the same period is Rs. $800$. The difference between the compound and simple interest for $3$ years will be ?
  1. $66.67$
  2. $36$
  3. $98.56$
  4. $60$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

SI for 2 years = 800, so SI for 1 year = 400. CI for 2 years = 832. The difference of 32 is the interest on the first year's interest (400). Rate = 32/400 = 8%. For 3 years, CI - SI = P * r^2 * (3 + r) / 100^2. P = 400 / 0.08 = 5000. Difference = 5000 * (0.08)^2 * (3.08) = 5000 * 0.0064 * 3.08 = 32 * 3.08 = 98.56.

Multiple choice

A certain sum is interested at compound interest . The interest occurred in the first two years is Rs. $272$ and that in the First three years is Rs. $434$. Find the rate $\%$ ?
  1. $33.33$ $\%$
  2. $25$ $\%$
  3. $12.5$ $\%$
  4. $16.67$ $\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The interest earned in the third year is 434 - 272 = Rs. 162. Let the annual rate be r and compare the third-year interest with the total interest for the first two years. Solving the resulting equation gives r = 12.5%.

Multiple choice

The difference between the amount of compound interest and simple interest accured on an amount of Rs. $26000$ at the end of $3$ years is Rs. $2994.134$. What is the rate of interest ?
  1. $22 \%$
  2. $17 \%$
  3. $19 \%$
  4. $24 \%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 3 years, the difference between compound interest and simple interest is given by the formula D = P * (r/100)^2 * (3 + r/100). Plugging in D = 2994.134 and P = 26000, we solve for r. Testing 19 percent: 26000 * (0.19)^2 * (3.19) = 26000 * 0.0361 * 3.19 = 2994.134.

Multiple choice

Leona bought a $1$-year, $\$10,000$ certificate of deposit that paid interest at an annual rate of $8$ percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
  1. $\$$10464
  2. $\$864$
  3. $\$816$
  4. $\$800$
  5. $\$480$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With semiannual compounding, the interest rate per period is 8% / 2 = 4%, and there are 2 periods in 1 year. The maturity value is 10,000 * (1.04)^2 = 10,816 dollars. Subtracting the principal of 10,000 dollars gives a total interest of 816 dollars.

Multiple choice

John deposited $\ $10,000$ to open a new savings account that earned $4$ percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account $6$ months after the account was opened?
  1. $\ $10,100$
  2. $\ $10,101$
  3. $\ $10,200$
  4. $\ $10,201$
  5. $\ $10,400$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The interest is 4% annually, compounded quarterly, so the quarterly rate is 1%. Over 6 months (2 quarters), the amount is 10000 * (1.01)^2 = 10000 * 1.0201 = 10201.

Multiple choice

The difference between the compound interest and the simple interest earned on a sum of money at the end of $4$ years is $Rs.256.40$. find the sum . Which of the following information given in the statements P and Q is / are necessary P: Amount of simple interest after $4$ years Q: Rate of interest per annum

  1. Only P is necessary

  2. Only Q is necessary

  3. Both P & Q are necessary

  4. Neither of P & Q are necessary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between CI and SI for 2 years is P(r/100)^2. For 4 years, the formula is more complex, involving the rate r. Without the rate, the difference cannot be used to find the sum P, even if SI is known. Thus, Q is necessary.

Multiple choice

An amount of money was lent for $3$ years. what will be the difference between the simple and the compound interest earned on it at the same rate? P : The rate of interest was $8\%$per annum. Q : The total amount of simple interest was Rs.$1200$

  1. Only P is sufficient to answer

  2. Only Q is sufficient to answer

  3. Both P & Q are sufficient to answer

  4. None of the above.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the difference between simple and compound interest for 3 years, you need the principal (P), the rate (R), and the time (T). Statement P provides the rate, and Statement Q provides the total simple interest, which allows calculating the principal. Both are necessary to determine the specific interest difference.