Question

When Cash Price is not given
6. Calculate cash price of a machine from the following information:

a) ₹10,000 -Down payment
b) 4 annual instalments at the end of each year -10,000
c) Rate of interest 5% p.a.​

Answer 1

Answer: The cash of the machine is Rs.45579

Explanation:

The following are the given details:

Down payment = 10000

4 Annual payments = 10000

Rate of interest = 5%

So you need to create this payment schedule backward from down to top.

Interest included in the 4th installment is to be calculated.

$Interest = \frac{Amt\ of\ installement\ + \ Interest}{100+\ interest}$

$=\frac{10000 * 5}{100+5}$

$=\frac{50000}{105}$

$= 476$

$Principle = 10000-476$

$=9524$

The amount of 4th installment = 9524

Interest included in the 3rd installment is to be calculated.

$Interest = \frac{Amt\ of\ installement\ + \ Interest}{100+\ interest}$

$=\frac{(10000+9524) * 5}{100+5}$

$=\frac{(19524)*5}{105}$

$= \frac{97620}{105}$

$=929$

$Principle = 10000-929$

$= 9070$

The amount of 3rd installment = 9070

Interest included in the 2nd installment is to be calculated.

$Interest = \frac{Amt\ of\ installement\ + \ Interest}{100+\ interest}$

$=\frac{(10000+9524+9070) * 5}{100+5}$

$=\frac{28594*5}{105}$

$= \frac{142970}{105}$

$= 1361$

$Principle = 10000-1361$

$= 8638$

The amount of 2nd installment = 8638

Interest included in the 1st installment is to be calculated.

$Interest = \frac{Amt\ of\ installement\ + \ Interest}{100+\ interest}$

$=\frac{(10000+9524+9070+8638) * 5}{100+5}$

$=\frac{37232*5}{105}$

$=\frac{186160}{105}$

$= 1772$

$Principle = 10000-1772$

$= 8227$

The amount of 1st installment = 8227

There the amount of

4th installment is 9524

3rd installment is 9070

2nd installment is 8638

1st installment is  8227

How to calculate the cash price we have to add all the installment amount and also the down payment amount

= 4th + 3rd + 2nd + 1st + Down payment

$= 9524+9070+8638+8227+10000$

$= 45579$

Therefore the cash price is 45579

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