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

If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70/r years. If Pat's parents invested $5000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
  1. $ $ 20,000$
  2. $ $ 15,000$
  3. $ $ 12,000$
  4. $ $ 10,000$
  5. $ $ 9,000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rule of 70 states that money doubles in 70/8 = 8.75 years. In 18 years, the money doubles approximately twice (18 / 8.75 is slightly more than 2). Doubling \$5000 twice results in \$5000 * 2 * 2 = $20,000.

Multiple choice

A certain sum of money is invested at 8% compound interest. If the compound interest for the first year is Rs. 100, find the compound interest for the 3rd year ________________.

  1. Rs. 116.64

  2. Rs. 116.00

  3. Rs. 120

  4. Rs. 108
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal P. Interest for 1st year = P * 0.08 = 100, so P = 1250. Amount after 1st year = 1350. Interest for 2nd year = 1350 * 0.08 = 108. Amount after 2nd year = 1350 + 108 = 1458. Interest for 3rd year = 1458 * 0.08 = 116.64.

Multiple choice

Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w?
  1. $\displaystyle \frac { w }{ 1+1.08 } $
  2. $\displaystyle \frac { w }{ 1.08+1.16 } $
  3. $\displaystyle \frac { w }{ 1.16+1.24 } $
  4. $\displaystyle \frac { w }{ 1.08+{ \left( 1.08 \right) }^{ 2 } } $
  5. $\displaystyle \frac { w }{ { \left( 1.08 \right) }^{ 2 }+{ \left( 1.08 \right) }^{ 3 } } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After 1 year, the account has x * 1.08. Then another x is added, so the balance is x * 1.08 + x. After the second year, this amount earns 8% interest: (x * 1.08 + x) * 1.08 = w. So, w = x * (1.08^2 + 1.08). Therefore, x = w / (1.08^2 + 1.08).

Multiple choice

$\displaystyle 1,000 \left( 1 + \frac{r}{1,200}\right)^{12}$ The expression above gives the amount of money, in dollars, generated in a year by a $\$1,000$ deposit in a bank account that pays an annual interest rate of $r\%$, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of $5\%$ than at an interest rate of $3\%$?
  1. $\displaystyle 1,000 \left(1 + \frac{5-3}{1,200}\right)^{12}$
  2. $\displaystyle 1,000 \left(1 + \frac{\displaystyle \frac{5}{3}}{1,200}\right)^{12}$
  3. $\displaystyle \frac{1,000 \left(1 + \displaystyle \frac{5}{1,200}\right)^{12}}{1,000 \left(1 + \displaystyle \frac{3}{1,200}\right)^{12}}$
  4. $\displaystyle 1,000 \left(1 + \displaystyle \frac{5}{1,200}\right)^{12} - \displaystyle 1,000 \left(1 + \displaystyle \frac{3}{1,200}\right)^{12}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The amount generated is A(r) = 1000 * (1 + r/1200)^12. Additional money at 5% vs 3% is A(5) - A(3).

Multiple choice

Susan invested certain amount of money in two schemes $A$ and $B$, which offer interest at the rate of $8\%$ per annum and $9\%$ per annum, respectively. She received Rs. $1860$ as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs. $20$ more as annual interest. How much money did she invest in each scheme?
  1. Rs. $13000 $   in scheme $A$, Rs. $12000$  in scheme $B$
  2. Rs. $12000$  in scheme $A$, Rs. $10000$ in scheme $B$
  3. Rs. $ 11000$  in scheme $A$, Rs. $10000$  in scheme $B$
  4. Rs. $10000$  in scheme $A$, Rs.  $13000$  in scheme $B$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

In the given question, a question is asked and is followed by three statements.While answering the question, you may or may not require the data provided in all the statements.You have to read, the question and the three statements and then decide whether the question can be answered with any one or two of the statements or all the three statements are required to answer the question.Select the correct option.What is the Principal sum ? (i) The sum amounts to Rs.690 in 3 years at S.I (ii) The sum amounts to Rs.750 in 5 years at S.I (iii) The rate of interest is $5\%$ p.a

  1. Both (i) and (iii)

  2. Both (ii) and (iii)

  3. Both (i) and (ii)

  4. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest (SI) = P * R * T / 100. (i) 690 = P + P * R * 3 / 100. (ii) 750 = P + P * R * 5 / 100. (iii) R = 5. With any two statements, we have two variables (P and R) or can solve for P using the difference in interest over time.

Multiple choice

If £500 is invested in a bank. In how many years will it amount to £608 if rate of interest is 4% compounded annually?

  1. 6 years

  2. 5 years

  3. 4 years

  4. 3 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the compound interest formula, we have 608 = 500 * (1.04)^n, which simplifies to 1.04^n = 1.216. Calculating the powers of 1.04, we find that 1.04^5 is approximately 1.2167, making 5 years the closest integer duration for the investment to reach 608.