At what rate percent a sum of 1600 amounts to 1933 after 2 years if interest is compounded half yearly?

In what time will the sum of Rs. 1600 at 5% p.a. CI amounts to Rs. 1764?A. 1B. 1.5C. 2D. 3

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In what time will the sum of Rs. 1600 at 5% p.a. CI amounts to Rs. 1764?A. 1B. 1.5C. 2D. 3
RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest
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Answer

Verified

Hint:
We know that the interest on the given principal is being compounded annually. So let use the formula of compound interest which is given below:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\], where P is the principal amount, R is the rate of interest and T is the time taken.

Complete step by step answer:
It is given in the problem that the principal amount is Rs.1600, the rate of interest is 5% compounded annually and the total amount becomes Rs.1764.
We have to find the time taken in which the principal rises to the amount Rs.1774
According to the question, we know that the sum invested is Rs. 1600 at a rate of 5% compounded annually. Assume the principal amount as P and the rate of interest
$P = Rs.1600$and$R = 5\% p.a.$
We need to calculate the time in which the principal rises to the amount Rs. 1774
\[A{\text{ }} = {\text{ }}Rs.{\text{ }}1774\]
We have the formula of the amount is:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]
Substituting the values of P, R, and A we get,
$1764 = 1600{\left( {1 + \dfrac{5}{{100}}} \right)^T}$
Simplifying the above equation:
$ \Rightarrow \dfrac{{1764}}{{1600}} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
$ \Rightarrow \dfrac{{441}}{{400}} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
$ \Rightarrow {\left( {\dfrac{{21}}{{20}}} \right)^2} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
By the law of exponents, we know that when the bases are the same across the equal too, the powers are equal. Thus we have,
$T = 2$
Hence, the principal will take 2 years to reach the amount to Rs.1764.
Therefore, option (C) is correct.

Note: The simple interest is cheaper than the compound interest because the simple interest applies to the whole amount for the whole time but in the case of compound interest, we have to pay the interest on the interest.

Jump to

Compound Interest Exercise 14.1
Compound Interest Exercise 14.2
Compound Interest Exercise 14.3
Compound Interest Exercise 14.4
Compound Interest Exercise 14.5

Rational Numbers
Powers
Squares and Square Roots
Cube and Cube Roots
Playing with Numbers
Algebraic Expressions and Identities
Factorization
Division of Algebraic Expressions
Linear Equation in One Variable
Direct and Inverse Variations
Time and Work
Percentage
Profit Loss Discount and Value Added Tax
Compound Interest
Understanding Shapes Polygons
Understanding Shapes Quadrilaterals
Understanding Shapes Special Types Quadrilaterals
Practical Goemetry
Visualising Shapes
Area of Trapezium and Polygon
Volume Surface Area Cuboid Cube
Surface Area and Volume of Right Circular Cylinder
Classification And Tabulation Of Data
Classification And Tabulation Of Data Graphical Representation Of Data As Histograms
Pictorial Representation Of Data As Pie Charts Or Circle Graphs
Data Handling Probability
Introduction To Graphs

RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest

Question 44 Compound Interest Exercise 14.2

In how much time will a sum of Rs. 1600 amount to Rs. 1852.20 at 5% perannum compound interest?

Answer:

Given details are,

Principal = Rs 1600

Amount = Rs 1852.20

Rate = 5% per annum

Let time = T years

By using the formula,

A = P (1 + R/100)^n

1852.20 = 1600 (1 + 5/100)^T

1852.20 = 1600 (105/100)^T

(21/20)^T = 1852.20/1600

(21/20)^T = 9261/8000

(21/20)^T = (21/20)^3

So on comparing both the sides, n = T = 3

∴ Time required is 3year

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Updated On: 27-06-2022

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