Question

A computer is available for rs. 39000 cash or rs. 17000 as cash down payment followed by five monthly installments of rs. 4800 each. What is the rate of interest per annum under the installment plant?

Answer 1

Given:

A computer is available for rs. 39000 cash or rs. 17000 as cash down payment followed by five monthly instalments of rs. 4800 each.

To find:

What is the rate of interest per annum under the instalment plant?

Solution:

The cost of the computer = Rs. 39000

The amount available as a down payment = Rs. 17000

∴ The balance amount = Rs. 39000 - Rs. 17000 = Rs. 22000

Let "R%" represent the rate of interest p.a.

We know the formula of S.I. is as follows:

• $S.I. =\frac{PRT}{100}$

• $Amount = P + S.I.$

∴ Amount on the balance amount of Rs. 22000 for 5 months  will be,

= $22000 + \frac{22000 \times R \times \frac{5}{12} }{100}$

= $22000 + (220 \times R \times \frac{5}{12} )$

= $22000 + ( \frac{1100 \times R }{12} )$

= $\bold{22000 + ( \frac{275 \times R }{3} )}$ ....... (i)

According to the question, the customer pays 5 monthly instalments of Rs. 4800 each to the shopkeeper, so, we get,

The total amount of instalments after 5 months will be,

= [Amount after 1st month] + [Amount after 2nd month] + [Amount after 3rd month] + [Amount after 4th month] + [Amount after 5th month]

 $= [4800 + \frac{4800\times R\times \frac{4}{12} }{100} ] \:+ \:[4800 + \frac{4800\times R\times \frac{3}{12} }{100}] \:+ \:[4800 + \frac{4800\times R\times \frac{2}{12} }{100}] \:+\: [4800 + \frac{4800\times R\times \frac{1}{12} }{100}] \:+\: [4800]$

$= [4800 + 16R ] \:+ \:[4800 + 12R} \:+ \:[4800 + 8 R] \:+\: [4800 + 4R] \:+\: [4800]$

$= [4800 \times 5] + [16R + 12R +8R+4R]$

$= \bold{24000 + 40R}$ ..... (ii)

Now, from (i) & (ii), we get

$22000 + ( \frac{275 \times R }{3} ) = 24000 + 40R$

$\implies \frac{275 R }{3} - 40 R = 24000 - 22000$

$\implies \frac{275 R - 120R}{3} = 2000$

$\implies 275 R - 120R = 6000$

$\implies 155R = 6000$

$\implies R = \frac{6000}{155}$

$\implies \bold{R = 38.7096\%}$ ≈ $\bold{38.71\%\:p.a.}$

Thus, the rate of interest per annum under the instalment plan is 38.71%.

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