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 mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

On a certain Principal if the Simple interest for two years is $Rs.\ 4800$ and Compound interest for the two years is $Rs.\ 5088$, what is the rate of interest

  1. $6\%$
  2. $24\%$
  3. $12\%$
  4. $18\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,  $SI=4800$
            $CI=5088$
Say the principal amount was $P$ and rate of interest is $r$% p.a for two years
$\therefore$   $SI=\dfrac { PT }{ 100 } =\dfrac { P\times 2\times r }{ 100 } $
$\Rightarrow 4800=\dfrac { 2Pr }{ 100 } $
$\Rightarrow 240000=Pr\quad \longrightarrow \left( 1 \right) $
Similarly $CI=P{ \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-P$
$\Rightarrow 5088=P\left[ { \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-1 \right] \quad \longrightarrow \left( 2 \right) $
Substituting $(1)$ in $(2)$ we get
$5088=\dfrac { 240000 }{ r } \left[ 1+\dfrac { { r }^{ 2 } }{ { 100 }^{ 2 } } +\dfrac { 2r }{ 100 } -1 \right] $
$\Rightarrow \dfrac { 5088 }{ 240000 } =\dfrac { r }{ { 100 }^{ 2 } } +\dfrac { 2 }{ 100 } $
$\Rightarrow 0.0212=\dfrac { r }{ { 100 }^{ 2 } } +0.02$
$\Rightarrow 0.0012=\dfrac { r }{ { 100 }^{ 2 } } $
$\therefore$    $r=12$%
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A sum of money compounded annually amounts to 1375 in 5 years and 1980 in 7 years. Find the annual rate of interest.

  1. 12%

  2. 20%

  3. 15%

  4. 10%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

interest is compounded, Amount $ A = P(1+ \frac {R}{100})^n $
So, for the first situation
$ 1375 = P \times (1+ \frac {R}{100})^5 $   - (1)

And for the first situation
$ 1980 = P \times (1+ \frac {R}{100})^7 $   ---- (2)

Dividing eqn 2 by eqn 1, we get
$ \frac {1980}{1375} =   (1+ \frac {R}{100})^2 $ 
$ => \frac {396}{275} =   (1+ \frac {R}{100})^2 $ 
$ => \frac {36}{25} =   (1+ \frac {R}{100})^2 $ 
$ => (1+ \frac {R}{100}) = \frac {6}{5} $
$ => \frac {R}{100} = \frac {1}{5} $
$ => R =20 $ %

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The difference between the interest earned under compound interest, interest being compounded annually and simple interest for two years on the same sum and at the same rate of interest is 25.60. Find the sum if the rate of interest is 8% p.a

  1. 2000

  2. 2500

  3. 3200

  4. 4000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation



Simple Interest $ SI = \frac {PNR}{100} $
So, $ SI = \frac {P \times 2 \times 8}{100} = Rs 0.16P $

When interest is compounded, Amount $ A = P(1+ \frac {R}{100})^n $
So, A $ = P \times (1+ \frac {8}{100})^2 = Rs  1.1664P  $
And $ CI = A - P = 0.1664P $

Si, difference $ CI - SI = Rs 0.1664P - Rs 0.16P = Rs 25.60 $
$ => 0.0064P = 25.60 $
$ => P = Rs  4000 $

Multiple choice commercial studies money loans from banks and financial institutions introduction to money - barter system owned fund and borrowed fund

_______ of a given sum of money due at the end of a certain period of time is that sum which if invested now at the given rate of interest accumulates to the given sum at the end of the period.

  1. Annuity

  2. Interest

  3. The present value

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

The present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return.

Multiple choice

A sum of money doubles itself in 10 years at a certain rate of simple interest. What is the rate of interest per annum?

  1. 5%

  2. 10%

  3. 15%

  4. 20%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the sum of money be P and the rate of interest be r. According to the question, P * (1 + r * 10) = 2P. Dividing both sides by P, we get 1 + r * 10 = 2. Subtracting 1 from both sides, we get r * 10 = 1. Therefore, r = 1 / 10 = 0.1 = 10%.

Multiple choice

A sum of money becomes (\frac{13}{12}) of itself in 2 years at a certain rate of simple interest. What is the rate of interest per annum?

  1. 6%

  2. 8%

  3. 10%

  4. 12%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simple Interest = (Principal * Rate * Time) / 100. Let the principal be (P) and the rate of interest be (R\%). In 2 years, the amount becomes (\frac{13}{12}P). Therefore, (\frac{13}{12}P = P + (P * R * 2) / 100). Simplifying the equation, we get (R = 12\%.

Multiple choice

What is the present value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 5%? (Assume continuous compounding.)

  1. $$\frac{1000}{0.05}$$
  2. $$\frac{1000}{0.05} \left( 1 - e^{-0.05 \cdot 10} \right)$$
  3. $$\frac{1000}{0.05} \left( e^{0.05 \cdot 10} - 1 \right)$$
  4. $$\frac{1000}{0.05} \left( e^{-0.05 \cdot 10} - 1 \right)$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The present value of an annuity that pays $1000 per year for 10 years at an annual interest rate of 5% (assuming continuous compounding) is $$\frac{1000}{0.05} \left( 1 - e^{-0.05 \cdot 10} \right)$$.

Multiple choice

What is the monthly payment on a loan of $100,000 that is to be repaid over 30 years at an annual interest rate of 4%? (Assume continuous compounding.)

  1. $$\frac{100,000}{30 \cdot 12}$$
  2. $$\frac{100,000}{30 \cdot 12} \left( 1 - e^{-0.04 \cdot 30} \right)$$
  3. $$\frac{100,000}{30 \cdot 12} \left( e^{0.04 \cdot 30} - 1 \right)$$
  4. $$\frac{100,000}{30 \cdot 12} \left( e^{-0.04 \cdot 30} - 1 \right)$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The monthly payment on a loan of $100,000 that is to be repaid over 30 years at an annual interest rate of 4% (assuming continuous compounding) is $$\frac{100,000}{30 \cdot 12} \left( 1 - e^{-0.04 \cdot 30} \right)$$.

Multiple choice

What is the effective annual interest rate on a loan that has a nominal annual interest rate of 12% and is compounded monthly?

  1. $$12\%$$
  2. $$12.68\%$$
  3. $$13.38\%$$
  4. $$14.10\%$$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The effective annual interest rate on a loan that has a nominal annual interest rate of 12% and is compounded monthly is $$13.38\%$$.

Multiple choice

What is the doubling time of an investment that is continuously compounded at an annual interest rate of 7%? (Assume that the initial investment is $1.)

  1. $$10\text{ years}$$
  2. $$11\text{ years}$$
  3. $$12\text{ years}$$
  4. $$13\text{ years}$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The doubling time of an investment that is continuously compounded at an annual interest rate of 7% is $$10\text{ years}$$. This means that it will take 10 years for the investment to double in value.

Multiple choice

What is the future value of an investment of $1000 that is continuously compounded at an annual interest rate of 5% for 10 years?

  1. $$\$1628.89$$
  2. $$\$1643.85$$
  3. $$\$1659.05$$
  4. $$\$1674.49$$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The future value of an investment of $1000 that is continuously compounded at an annual interest rate of 5% for 10 years is $$\$1643.85$$. This means that the investment will be worth $1643.85 at the end of 10 years.

Multiple choice

What is the present value of an investment that will be worth $1000 in 10 years if the annual interest rate is 5% and the interest is compounded continuously?

  1. $$\$783.53$$
  2. $$\$789.34$$
  3. $$\$795.27$$
  4. $$\$801.33$$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The present value of an investment that will be worth $1000 in 10 years if the annual interest rate is 5% and the interest is compounded continuously is $$\$783.53$$. This means that you would need to invest $783.53 today in order to have $1000 in 10 years.