    # What is the compound interest on Rs 31250 at 8% per annum for 2 years?

2

Present value, P = Rs.31250

Interest rate, R = 8% per annum

Time, n = (3/2) years

Compounded half-yearly.

Amount (A) = P [1 + (R/2)/100]2n [Where, P = Present value

R = Annual interest rate

n = Time in years]

A = 31250 [1 + (8/2)/100]3 [2n = 2 × 3/2]

A = 31250 [1 + 4/100]3

A = 31250 [1 + 1/25]3

A = 31250 [26/25]3

A = 31250 × 17576/15625

A = 2 × 17576

A = 35152

Amount = Rs.35152

Compound interest = Rs.(35152 – 31250) [CI = A – P]

= Rs.3902

### 1. Find the amount of \$ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.

Solution: Here, P = \$ 8000, R = 5 % per annum and n = 3 years. Using the formula A = \$ P(1 + R/ 100)ⁿ amount after 3 years = \$ {8000 × (1 + 5/100)³} = \$ (8000 × 21/20 × 21/20 × 21/20) = \$ 9261. Thus, amount after 3 years = \$ 9261. And, compound interest = \$ (9261 - 8000)

Therefore, compound interest = \$ 1261.

### 2. Find the compound interest on \$ 6400 for 2 years, compounded annually at 7¹/₂ % per annum.

Solution: Here, P = \$ 6400, R % p. a. and n = 2 years. Using the formula A = P (1 + R/100)ⁿ Amount after 2 years = [6400 × {1 + 15/(2 × 100)}²] = \$ (6400 × 43/40 × 43/40) =\$ 7396. Thus, amount = \$ 7396 and compound interest = \$ (7396 - 6400)

Therefore, compound interest = \$ 996.

Case 2: Let principal = \$ P, time = 2 years, and let the rates of interest be p % p.a. during the first year and q % p.a. during the second year.

Then, amount after 2 years = \$ {P × (1 + P/100) × (1 + q/100)}. This formula may similarly be extended for any number of years.

### 1. Find the amount of \$ 12000 after 2 years, compounded annually; the rate of interest being 5 % p.a. during the first year and 6 % p.a. during the second year. Also, find the compound interest.

Solution: Here, P = \$12000, p = 5 % p.a. and q = 6 % p.a. Using the formula A = {P × (1 + P/100) × (1 + q/100)} amount after 2 years = \$ {12000 × (1 + 5/100) × (1 + 6/100)} = \$ (12000 × 21/20 × 53/50) =\$ 13356 Thus, amount after 2 years = \$ 13356 And, compound interest = \$ (13356 – 12000)

Therefore, compound interest = \$ 1356.

Case 3: For example suppose time is 2³/₅ years then,

Amount = P × (1 + R/100)² × [1 + (3/5 × R)/100]

### 1. Find the compound interest on \$ 31250 at 8 % per annum for 2 years. Solution Amount after 2³/₄ years

Solution: Amount after 2³/₄ years = \$ [31250 × (1 + 8/100)² × (1 + (3/4 × 8)/100)] = \${31250 × (27/25)² × (53/50)} = \$ (31250 × 27/25 × 27/25 × 53/50) = \$ 38637. Therefore, Amount = \$ 38637, Hence, compound interest = \$ (38637 - 31250) = \$ 7387.

Let principal = \$ P, rate = R% per annum, time = a years.

Suppose that the interest is compounded half- yearly.

Then,

rate = (R/2) % per half-year, time = (2n) half-years, and amount = P × (1 + R/(2 × 100))²ⁿ

Compound interest = (amount) - (principal).

### 1. Find the compound interest on \$ 15625 for 1¹/₂ years at 8 % per annum when compounded half-yearly.

Solution: Here, principal = \$ 15625, rate = 8 % per annum = 4% per half-year, time = 1¹/₂ years = 3 half-years. Amount = \$ [15625 × (1 + 4/100)³] =\$ (15625 × 26/25 × 26/25 × 26/25)= \$ 17576. Compound interest = \$ (17576 - 15625) = \$ 1951.

### 2. Find the compound interest on \$ 160000 for 2 years at 10% per annum when compounded semi-annually.

Solution: Here, principal = \$ 160000, rate = 10 % per annum = 5% per half-year, time = 2 years = 4 half-years. Amount = \$ {160000 × (1 + 5/100)⁴} =\$ (160000 × 21/20 × 21/20 × 21/20 × 21/20) compound interest = \$ (194481- 160000) = \$ 34481.

### Interest Compounded Quarterly

Then,

rate = (R/4) % Per quarter, time = (4n) quarters, and amount = P × (1 + R/(4 × 100))⁴ⁿ

Compound interest = (amount) - (principal).

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In 8th grade math practice you will get all types of examples on different topics along with the solutions. 8th grade math worksheets are arranged in such a way that students can learn math while practicing it step by step.

Keeping in mind the mental level of child in 8th grade, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts.

In 8th grade math test we need to learn Rational Numbers, Exponents, Square and Square Roots, Cubes and Cube roots, Operations on Algebraic Expressions, Factorization, Linear Equations, Profit and Loss, Compound Interest, Ratio and Proportion, Time and Work and in geometry we learn Quadrilaterals, Parallelograms, Construction of Quadrilaterals, Three-Dimensional Figures, Area of a Trapezium and a Polygon, Volume and Surface Area of Solids, Data Handling, Constructing and Interpreting Bar Graphs, Pie Charts, Probability, Graphs, etc……

If student follow math-only-math they can improve their knowledge by practicing the worksheets for 8th graders which will them to score in their exam.

Set Theory

Sets Theory: Brief description on set theory and the important sets used in mathematics.

Representation of a Set: Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Types of Sets: Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Finite Sets and Infinite Sets: Learn how to distinguish between finite set and infinite set with examples.

Power Set: Explanation on power sets will help us to get the basic concepts if sets with examples.

Problems on Union of Sets: Learn how to find the union of two or more sets and worked-out examples of operations on union of sets.

Problems on Intersection of Sets: Learn how to find the intersection of two or more sets and worked-out examples of operations on intersection of sets.

Difference of two Sets: Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set: Definition of complement of a set and their properties with some worked-out examples.

Problems on Complement of a Set: Learn how to find the complement of two or more sets and worked-out examples of operations on complement of sets.

Problems on Operation on Sets: Learn how to find the union and intersection of two or more sets and worked-out examples of the two basic operations of sets.

Word Problems on Sets: Apply set operations to solve word problems involving the properties of union and intersection of sets.

Venn Diagrams in Different Situations: Learn how to use the Venn diagrams in different situations to find the different sets.

Relationship in Sets using Venn Diagram: Learn how to find the relationship of the union, intersection and difference of the two sets using Venn-diagram.

Union of Sets using Venn Diagram: Diagrammatic representation to find the union of two sets and their properties, worked-out examples.

Intersection of Sets using Venn Diagram: Diagrammatic representation to find the intersection of two sets and their properties, worked-out examples.

Disjoint of Sets using Venn Diagram: Learn how to represent the disjoint sets of union and intersection using Venn-Diagram.

Difference of Sets using Venn Diagram: Learn how to represent the difference between two sets using Venn-Diagram.

Examples on Venn Diagram: Learn how to use the basic concepts of sets for solving the different types of problems on Venn diagram.

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Simple Interest Worksheet

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