Answer
Verified
468k+ views
Hint: Here we will proceed by assuming each instalment, m and n as variables. Then we will use the concept of deferred annuity to find each instalment using the given rate of interest i.e. 12% and principal amount be Rs. 20,000.
Complete step-by-step answer:
Deferred annuity is an annuity which commences only after a lapse of some specified time after the final purchase premium has been paid.
Formula of deferred annuity –
$p = \dfrac{a}{i}\dfrac{{{{\left( {1 + i} \right)}^n} - 1}}{{{{\left( {1 + i} \right)}^{m + n}}}}$
Here we will assume that each instalment will be a, m be the semi-annual instalment and n be the remaining instalments.
$ \Rightarrow $ m=7, n=3 and m + n=10,
Also given that p is Rs. 20,000
Now we will calculate i @ 12%,
$ \Rightarrow \dfrac{{12}}{{100}} \times \dfrac{1}{2} = 0.06$
So we will put the values of p, m + n and i in the formula,
$ \Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{{{\left( {1 + 0.06} \right)}^7} - 1}}{{{{\left( {1 + 0.06} \right)}^{10}}}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{{{\left( {1.06} \right)}^7} - 1}}{{{{\left( {1 + 0.06} \right)}^{10}}}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{1.503 - 1}}{{1.791}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{0.503}}{{1.791}}$
$\Rightarrow a = \dfrac{{20,000 \times 0.06 \times 1.791}}{{0.503}}$
$\Rightarrow a = \dfrac{{2149.2}}{{0.503}}$
$\therefore a = 427.76$
Hence each instalment is of Rs. 427.67.
Note: In order to solve this question, one mistake that many of us can do is we do not convert the given rate into i i.e. instalment. Also we must be careful about the semi-annual instalment in which m is semi-annual instalment and n is remaining seven instalments as one can get confused in this statement. Hence we will get the desired result.
Complete step-by-step answer:
Deferred annuity is an annuity which commences only after a lapse of some specified time after the final purchase premium has been paid.
Formula of deferred annuity –
$p = \dfrac{a}{i}\dfrac{{{{\left( {1 + i} \right)}^n} - 1}}{{{{\left( {1 + i} \right)}^{m + n}}}}$
Here we will assume that each instalment will be a, m be the semi-annual instalment and n be the remaining instalments.
$ \Rightarrow $ m=7, n=3 and m + n=10,
Also given that p is Rs. 20,000
Now we will calculate i @ 12%,
$ \Rightarrow \dfrac{{12}}{{100}} \times \dfrac{1}{2} = 0.06$
So we will put the values of p, m + n and i in the formula,
$ \Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{{{\left( {1 + 0.06} \right)}^7} - 1}}{{{{\left( {1 + 0.06} \right)}^{10}}}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{{{\left( {1.06} \right)}^7} - 1}}{{{{\left( {1 + 0.06} \right)}^{10}}}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{1.503 - 1}}{{1.791}}$
$\Rightarrow 20,000 = \dfrac{a}{{0.06}} \times \dfrac{{0.503}}{{1.791}}$
$\Rightarrow a = \dfrac{{20,000 \times 0.06 \times 1.791}}{{0.503}}$
$\Rightarrow a = \dfrac{{2149.2}}{{0.503}}$
$\therefore a = 427.76$
Hence each instalment is of Rs. 427.67.
Note: In order to solve this question, one mistake that many of us can do is we do not convert the given rate into i i.e. instalment. Also we must be careful about the semi-annual instalment in which m is semi-annual instalment and n is remaining seven instalments as one can get confused in this statement. Hence we will get the desired result.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Which are the Top 10 Largest Countries of the World?
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE