- A steel container is sold at Rs 120 cash or Rs 25 as cash down payment and Rs 25 a month for 4 months. The rate of interest per annum charged under the instalment plan is
• To calculate the rate of interest per annum charged under the instalment plan, we need to calculate the equivalent annual rate of interest (EAR).
• The equivalent annual rate of interest (EAR) is the rate of interest that is equivalent to the series of payments made during the year.
• The equivalent annual rate of interest (EAR) is used to compare different loans and investments.
• The EAR is the rate of interest which would be earned if the payments were made in the same order but in one year.
• To calculate the equivalent annual rate of interest (EAR), the following formula can be used:
EAR = [P(1+i)n -1] / [P (n-1)]
Where:
P = Principal amount
i = periodic rate
n = number of payments
• In the given question, we are given the following information:
Cash price = Rs.120
Cash down payment = Rs. 25
Number of payments = 4
• We need to calculate the periodic rate (i)
• Substituting the given values in the formula, we get:
EAR = [25 (1+i)4 -1] / [25 (4-1)]
• Solving for i, we get
i = (1.2609 - 1) / (1 + 4)
i = 0.0609
• Therefore, the periodic rate (i) is 0.0609
• To calculate the rate of interest per annum (EAR), we need to convert the periodic rate (i) to annual rate (EAR).
• To convert the periodic rate (i) to annual rate (EAR), the following formula can be used:
EAR = (1 + i)n – 1
• Substituting the given values in the formula, we get:
EAR = (1 + 0.0609)4 – 1
EAR = (1.2609 – 1)
EAR = 0.2609
• Therefore, the rate of interest per annum charged under the instalment plan is 26.09%.
Hence, the correct answer is Option C: 26.09%.
If you think the solution is wrong then please provide your own solution below in the comments section .
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25 rupees down payment means 95 rupees is what we are "Borrowing" from the shop.
Amount paid in instalments = 25 * 4 = 100
So 100 - 95 = 5 is the interest
Now this interest gained (Rs 5) is through the interest gained in the available amount month by month.
let R is the rate of interst P.A. (and R/12 per month)
5 = 95R/(12 * 100) + 70R/(12 * 100) + 45R/(12 * 100) + 20R/(12 * 100)
5 = 230R/(12 * 100)
R = 6000/230 = 26.09%
Downpatment 25
120-25 =95
25 gives 4 equal amount
95-25=70
70-25=45
45-25=20
20-25=5
It gives 5 rs extra it is a interest
Then
(95×r+70×r+45×r+20×r)/12×100=5
R=26.09