• 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 .

The given problem can be solved by using the concept of Present Value (PV) of Annuity.

Present Value of Annuity: Present Value of Annuity (PV) is the present value of the future payments (instalments) which are to be made at regular intervals, discounted at a given rate of interest. Mathematically, it can be expressed as:

PV = A {[1 – (1 + r)-n]/r}

Where,
A = Annuity
r = Rate of Interest
n = Number of Periods

Given,
A = Rs. 7500
r = 4% p.a.
n = 3

Substituting the values in the above formula,
PV = 7500 {[1 – (1 + 0.04)-3]/0.04}
PV = 7500 {[1 – 0.9306]/0.04}
PV = 7500 {[0.0694]/0.04}
PV = 7500 x 17.35
PV = Rs. 13026.25

Therefore, the present value of the three annual instalments of Rs. 7500 is Rs. 13026.25.

The amount of each annual instalment can be calculated by dividing the present value of annuity by the number of periods.

Amount of each Instalment = 13026.25/3
Amount of each Instalment = Rs. 2702.61

Hence, the amount of each annual instalment is Rs. 2702.61.

If you think the solution is wrong then please provide your own solution below in the comments section .