A machinery supplier is offering a certain machinery on a 10% downpayment and the balance payable in equal end of the year payments without interest for 2 years. Under this arrangement, the price is pegged to be P 250,000. However, for cash purchase, the machine would only cost P 195,000. What is the equivalent interest rate that is being charged on the 2-year payment plan if interest is compounded quarterly?

Question

A machinery supplier is offering a certain machinery on a 10% downpayment and the balance payable in equal end of the year payments without interest for 2 years. Under this arrangement, the price is pegged to be P 250,000. However, for cash purchase, the machine would only cost P 195,000. What is the equivalent interest rate that is being charged on the 2-year payment plan if interest is compounded quarterly?

Answer 1

Let's solve this problem step by step.

First, let's find the downpayment amount. The downpayment for the machinery is 10% of the total price, which is 10/100 * 250,000 = P 25,000.

Next, let's find the total balance that needs to be paid in equal end of the year payments. The total price of the machinery is P 250,000, and the downpayment is P 25,000. So, the balance is 250,000 - 25,000 = P 225,000.

Now, let's find the quarterly payments. Since there are 2 years of payment, there will be 2 end of the year payments. Therefore, there will be 2 years * 4 quarters = 8 quarterly payments. So, the quarterly payment amount is 225,000 / 8 = P 28,125.

The cash purchase price of the machinery is P 195,000. This amount is paid immediately, so there is no need to calculate the interest rate for this.

Now, let's find the interest rate for the 2-year payment plan.

To find the interest rate compounded quarterly, we can use the formula:

FV = PV * (1 + r)^n

Where:
FV = Future Value (balance amount)
PV = Present Value (downpayment amount)
r = Interest rate per compounding period
n = Number of compounding periods

We know that FV = P 225,000, PV = P 25,000, r = ? and n = 8

225,000 = 25,000 * (1 + r)^8

Dividing both sides by 25,000:

9 = (1 + r)^8

Taking the 8th root of both sides:

(1 + r) = 9^(1/8)

Subtracting 1 from both sides:

r = 9^(1/8) - 1

Using a calculator, we can find that r is approximately 0.0927.

To get the equivalent interest rate, we multiply r by the number of compounding periods in a year (4 quarters) to get:

Equivalent interest rate = 0.0927 * 4 = 0.3708 = 37.08%

So, the equivalent interest rate being charged on the 2-year payment plan is approximately 37.08%.