GMAT / GRE Mathematics Tutorial Series: Simple And Compound Interest

Simple and Compound Interest Problems

The concept of compounding is widely used in the financial domain where the value of an investment increases exponentially over a given period of time. It’s also the underlying principle of several MBA topics such as time value of money and discounted cash flow (DCF) valuation.

Being thorough in this concept will not only help you in the entrance exams but it will also help you in making wise decisions with regard to your investments.

Also Check GMAT / GRE Tutorial Series Profit And Loss

Simple and Compound interest Problems and Solutions

These are some of the basic definitions and formulas to solve problems on Interest.

Principal: This refers to the sum of money that is lent or borrowed.

Interest: This is expressed as a percentage and it refers to the money earned on savings or extra money to be paid for the sum borrowed.

Say, the interest is 20% on a loan of Rs. 100. Then the interest in the amount is Rs. 20 and at the end of the year, the amount to be paid is Rs. 120.

Time: This refers to the time period for which the money is lent or the time period within which the sum of money has to be returned with interest.

Also Check GMAT / GRE Tutorial Series Quadratic Equation

Simple Interest

As the name suggests, the calculation of GMAT Exam simple and Compound interest Questions is quite simple.

It involves multiplying the principal amount with the number of years and the rate of interest.

Simple Interest Formula:

Simple Interest = Principal * Time * Rate of interest / 100

Abbreviated as SI = PTR/100

Compound Interest

In compound interest, the interest earned is reinvested in the next period of time. Or in other words, compound interest is calculated on the principal amount and the accumulated interest of the previous period.

Consider an amount is compounded annually for 2 years; the principal amount with interest gained at the end of first year becomes the principal for the second year.

Compound Interest Formula:

Amount = Principal * [1 + Rate of Interest/100]Time period

Abbreviated as Amount = P * [1 + R/100]t, when compounded annually.

Sometimes, the interest is also calculated half-yearly or quarterly.

When compounded semi-annually or half-yearly,

Amount = P [1 + (R/2)/100]2t

When compounded quarterly,

Amount = P [1 + (R/4)/100]4t

The present worth of Principal P due ‘ t’ years hence is given by:

P/[1+ R/100]t

Also Check GMAT / GRE Mathematics Tutorial Distance. Time and Speed

Sample problems and solutions

Let us solve some examples to understand this concept
 
Problem 1. A sum of Rs. 25000 invested becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.

Solution:

Simple interest = 27250 – 25000 = 2250

Time = 3 years.

SI = PTR / 100 → R = SI * 100 / PT

R = 2250 * 100 / 25000 * 3 → R = 3%.
 
Problem 2. What is the present value of Rs. 78000 due in 4 years at 5% interest per year.

Solution:

Amount with interest after 4 years = Rs. 78000

Therefore, simple interest = 78000 – Principal.

Let the principal amount be p.

78000 – p = p*4*5/100 → p=13000

Principal = 78000 – 13000 = Rs. 65000
 
Problem 3. A certain sum of money grows to Rs. 15000 in 2.5 years and to Rs. 16500 in 4 years at the same rate of interest. What is the rate of interest?

Solution:

The amount becomes 15000 in 2.5 years and 16500 in 4 years.

Simple interest for (4-2.5) years = 16500 – 15000

Therefore, SI for 1.5 years = Rs. 1500.

SI for 2.5 years = 1500/1.5 * 2.5 = 2500

Principal amount = 15000 – 2500 = Rs. 12500.

Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%.
 
Problem 4. Find the compound interest on a sum of Rs. 3000 at 5% for a period of 2 years, compounded annually.

Solution:

Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5

Therefore, CI = 3307.5 – 3000 = Rs. 307.5
 
Problem 5. Find the compound interest on Rs. 10000 at 12% rate of interest for 1 year, compounded half-yearly.

Solution:

Amount with CI = 10000 [1+ (12/2 * 100)]2 = Rs. 11236

Therefore, CI = 11236 – 10000 = Rs. 1236
 
Problem 6. The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. What will be the principal amount?

Solution:

Let the principal amount be x.

SI = x * 2 * 8 / 100 = 4x/25

CI = x[1+ 8/100]2 – x → 104x/625

Therefore, 104x/625 – 4x/25 = 12.80

Solving which gives x, Principal = Rs. 2000.
 
Problem 7. Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.

Solution:

Let the rate of interest be r.

5000[1+ r/100]2 = 5000+253.125

→ [1+r/100]2 = 5253.125/5000

Solving which gives

[1+ r/100]2 = 1681/1600

→ 1+r/100 = 41/40

→ r = 2.5

Therefore, SI = 5000* 2 * 2.5/ 100 = Rs. 250.
 
Problem 8. A certain sum amounts to Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?

Solution:

SI on Rs. 5760 for 1 year = 6912 – 5760 = Rs. 1152

Therefore, Rate of interest for 1 year = 100*1152/5760*1 = 20%

Let the principal be p.

Then, Principal = p[1+ 20/100]2 = 5760

Solving which gives Principal = Rs. 4000
 
Problem 9. How long does it take for a certain sum of money to increase by 30% at the rate of 15% simple interest?

Solution:

Let the principal be Rs. x

Simple interest = x*30/100 = 3x/10

T = 100*SI/PR = 100*3x/10 / x*15 = 2%

This can be solved by considering the principal amount to be Rs. 100. Then, SI = Rs. 30.

Then, T = 100*30/100*15 = 2% 

Practice problems

Problem 1

A banker lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year to a dealer. The amount must be returned to the banker when the total interest comes to Rs. 350. What is the number of years this will take?.

  • A. 3.5
  • B. 3.75
  • C. 4
  • D. 4.5

Answer A.

Explanation

(1000*t*3/100) + (1400*t*5/100) = 350 → t =3.5

Problem 2

Find the present value of Rs. 20872.5 due in 2 years at 10% rate of interest.

  • A. 17500
  • B. 17520
  • C. 17750
  • D. 17250

Answer D.

Explanation:

Present value = 20872.5/[1+ 10/100]2       

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