3 Marks Question

Question 13 Marks

A textile company has raised funds in the form of 5,000 zero-coupon bonds worth $₹ 1,100$ each. The company wants to set up a sinking fund for repayment of the bonds, which will be after 7 years. Determine the amount of the periodic contribution if the annualized rate of interest is $6 \%$, and the contribution will be done quarterly. [Given $(1.015)^{28}=1.5172$ ]

Answer

Given, Sinking fund,
$A=$ Par value of bond $\times$ No. of bonds
=₹ 1,100 x 5,000=₹ 5,500,000
No. of years, $n=7$
No. of payments per year, $m=4$
Annualized rate of interest, $r=6 \%$
$
\therefore \quad i=\frac{6}{400}=0.015
$
Therefore, the amount of the periodic contribution can be calculated using the above formula as,
$
P=A\left[\frac{i}{(1+i)^{n \times x m}-1}\right]
$
$\begin{array}{l}=55,00,000\left[\frac{0.015}{(1+0.015)^{28}-1}\right] \\ =55,00,000\left[\frac{0.015}{(1.015)^{28}-1}\right] \\ =55,00,000\left[\frac{0.015}{1.5172-1}\right]\end{array}$
$\begin{array}{l}=55,00,000\left[\frac{0.015}{0.5172}\right] \\ =55,00,000 \times 0.0290\end{array}$
=₹ 159512.76 ≈x ₹ 159513

View full question & answer→

Question 23 Marks

A company XYZ borrowed ₹ 1.5 lakhs for reformation. The company plans to set up a sinking fund that will pay back the loan at the end of 3 years. Assuming a rate of $9 \%$ compounded quarterly, and the sinking fund of the ordinary annuity. Given that $(1.0225)^{12}=1.3060$.

Answer

Given, P= ₹ 1,50,000, r=9 % or 0.09 ,
No. of years, $n=3$ years and No. of payments per year, $m=4$ (quarterly)
Sinking Fund,
$
\begin{aligned}
A & =\frac{\left[\left(1+\left(\frac{r}{m}\right)\right)^{n \times m}\right]-1}{\left(\frac{r}{m}\right)} \times P \\
& =\frac{\left[\left(1+\left(\frac{0.09}{4}\right)\right)^{12}\right]-1}{\left(\frac{0.09}{4}\right)} \times 1,50,000
\end{aligned}
$
$\begin{array}{l}=\frac{\left[(1+0.0225)^{12}\right]-1}{0.0225} \times 1,50,000 \\ =\frac{\left[(1.0225)^{12}\right]-1}{0.0225} \times 1,50,000\end{array}$
$\begin{array}{l}=\frac{1.3060-1}{0.0225} \times 1,50,000 \\ =\frac{0.3060}{0.0225} \times 1,50,000\end{array}$
= ₹ 2,040,000

View full question & answer→

Question 33 Marks

Riya invested ₹ 20,000 in a mutual fund in year 2016. The value of mutual fund increased to ₹ 32,000 in year 2021. Calculate the compound annual growth rate of her investment. [Given, $\log (1.6)=0.2041$, $\operatorname{antilog}(0.04082)=1.098]$

View full question & answer→

Question 43 Marks

Rohan purchased a laptop worth ₹ 80000 . He paid ₹ 20,000 as cash down and balance in equal monthly instalments in 2 years. If bank charges $9 \%$ p.a. compounded monthly. Calculate the EMI.

View full question & answer→

Question 53 Marks

A firm anticipates an expenditure of ₹ 50,0000 for plant modernization at end of 10 years from now. How much should the company deposit at the end of year into a sinking fund earning interest $5 \%$ per annum. [Given $\log 1.05=0.0212$, $\operatorname{antilog}(0.2120)=1.629]$

View full question & answer→

Question 63 Marks

An interviewer gives the following graph on a client's sales in the last 7 years to candidate and said find the CAGR. Given that $\left(\frac{9}{4}\right)^{\frac{1}{7}}=1.1228$.

Answer

Sales in 2006 were 0.8 crores (beginning value). In 2013, after 7 years, sales increased to 1.8 crores.
$
CAGR=\left(\frac{\text { End value }}{\text { Beginning value }}\right)^{\frac{1}{n}}-1
$
$\begin{array}{l}=\left(\frac{1.8}{0.8}\right)^{\frac{1}{7}}-1=\left(\frac{9}{4}\right)^{\frac{1}{7}}-1 \\ =0.1228\end{array}$
$CAGR \%=12.28 \%$

View full question & answer→

Applied Maths 3 Marks Question

Test yourself on this topic