Question:
What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[
\text{{Given: }} (1.03)^{16} = 1.6047
\]
What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]
Show Hint
For annuity calculations, use the compounded interest rate per period. Here, 6\% p.a. compounded semi-annually means \( r = 0.03 \) and the number of periods \( n = 16 \).
Updated On: June 02, 2025
- ₹ 3,432.53
- ₹ 2,783.08
- ₹ 2,480.57
- ₹ 2,149.93
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use the formula for future value of annuity:
\[
FV = R \cdot \frac{(1 + r)^n - 1}{r}.
\]
Rearrange to calculate \( R \):
\[
R = \frac{FV \cdot r}{(1 + r)^n - 1}.
\]
Step 2: Substitute values:
- \( FV = 50000 \),
- \( r = \frac{6\%}{2} = 0.03 \),
- \( n = 8 \times 2 = 16 \),
- Given \( (1.03)^{16} = 1.6047 \).
\[
R = \frac{50000 \times 0.03}{(1.03)^{16} - 1} = \frac{1500}{0.6047} \approx 2480.57.
\]
Was this answer helpful?
0
0
Top Questions on Vectors
- If the sum of two vectors is a unit vector, then the magnitude of their difference is:
- Let A be the point of intersection of the lines $$ L_1 : \frac{x - 7}{1} = \frac{y - 5}{0} = \frac{z - 3}{-1} \quad \text{and} \quad L_2 : \frac{x - 1}{3} = \frac{y + 3}{4} = \frac{z + 7}{5}$$ Let B and C be the points on the lines $ L_1 $ and $ L_2 $, respectively, such that $ AB - AC = \sqrt{15} $. Then the square of the area of the triangle ABC is:
- If the components of \( \vec{a} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k} \) along and perpendicular to \( \vec{b} = 3\hat{i} + \hat{j} - \hat{k} \) respectively are \( \frac{16}{11} (3\hat{i} + \hat{j} - \hat{k}) \) and \( \frac{1}{11} (-4\hat{i} - 5\hat{j} - 17\hat{k}) \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is equal to:
- Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:
- Let \( \vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}, \, \vec{b} = 3\hat{i} + \hat{j} - \hat{k} \) and \( \vec{c} \) be three vectors such that \( \vec{c} \) is coplanar with \( \vec{a} \) and \( \vec{b} \). If the vector \( \vec{c} \) is perpendicular to \( \vec{b} \) and \( \vec{a} \cdot \vec{c} = 5 \), then \( |\vec{c}| \) is equal to:
View More Questions
Questions Asked in CBSE CLASS XII exam
- If \( p \) and \( q \) are respectively the order and degree of the differential equation \( \frac{d}{dx} \left( \frac{dy}{dx} \right)^3 = 0 \), then \( (p - q) \) is:
- CBSE CLASS XII - 2025
- Differential Equations
- Show the refraction of light wave at a plane interface using Huygens' principle and prove Snell's law.
- CBSE CLASS XII - 2025
- Wave Optics
- The threshold voltage of a silicon diode is 0.7 V. It is operated at this point by connecting the diode in series with a battery of \( V \) volt and a resistor of 1000 \( \Omega \). Find the value of \( V \) when the current drawn is 15 mA.
- CBSE CLASS XII - 2025
- Semiconductor electronics: materials, devices and simple circuits
- Draw the structure of the major monohalo product for each of the following reactions:
- CBSE CLASS XII - 2025
- Haloalkanes And Haloarenes
- If a line makes angles of \( \frac{3\pi}{4} \) and \( \frac{\pi}{3} \) with the positive directions of \( x \), \( y \), and \( z \)-axes respectively, then \( \theta \) is:
View More Questions
