Question

The cost of the machine is Rs. 20,00,000, and if it is purchased under instalment basis; the company has to pay 25% of the cost at the time of purchase and the remaining amount in 10 annual equal instalments of Rs. 2,50,000 each. If rate of interest is 18%, compounded annually the present worth of the machine will be
1. Rs. 17,01,000
2. Rs. 16,22,500
3. Rs. 15,43,000
4. Rs. 14,64,500

Answer 1

Correct Answer - Option 2 : Rs. 16,22,500

Concept:

The present worth of machine, P is given by

\(P = I + A\frac{{\left\{ {{{\left( {1 + i} \right)}^n} - 1} \right\}}}{{i{{\left( {1 + i} \right)}^n}}}\)

Where,

I = is the initial payment

I is the rate of interest 

n is no of instalments

A is amount of each instalment

Calculation:

Given, I = 25 % of 20 lakh = Rs. 5 Lakh, i = 18%, n = 10 & A = Rs. 2.5 Lakh

\(P = 500000 + 250000 \times \frac{{\left\{ {{{\left( {1 + 0.18} \right)}^{10}} - 1} \right\}}}{{0.18 \times {{\left( {1 + 0.18} \right)}^{10}}}}\)

∴ P = Rs 1623521