A man purchased a car with a cash price of P 350,000. He was able to negotiate with the seller to allow him to pay only a downpayment of 20% and the balance payable in equal 48 end of the month installment at 1.5% interest per month. One the day he paid the 20th installment, he decided to pay monthly payment. What is the remaining balance that he paid?
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?
For the car purchase:
The downpayment for the car is 20% of P 350,000 = P 70,000.
So the remaining balance is P 350,000 - P 70,000 = P 280,000.
The interest per month is 1.5% of the remaining balance, so the interest per month is 1.5/100 * P 280,000 = P 4,200.
The total interest paid for the 48-month installment is P 4,200 x 48 = P 201,600.
The total amount to be paid for the car is P 350,000 + P 201,600 = P 551,600.
On the 20th installment, he decided to pay the monthly payment.
The monthly payment is P 551,600/48 = P 11,491.67.
He already paid P 11,491.67 x 20 = P 229,833.33.
The remaining balance that he paid is P 551,600 - P 229,833.33 = P 321,766.67.
Therefore, the remaining balance that he paid is P 321,766.67.
For the machinery purchase:
The downpayment for the machinery is 10% of P 250,000 = P 25,000.
So the remaining balance is P 250,000 - P 25,000 = P 225,000.
The equivalent interest rate that is being charged on the 2-year payment plan if interest is compounded quarterly can be calculated using the formula for compound interest:
P = A * (1 + r/n)^(nt)
Where:
P = Principal amount (P 225,000)
A = Amount after interest has been added to the principal (P 250,000)
r = annual interest rate (unknown)
n = number of times that interest is compounded per year (4, since interest is compounded quarterly)
t = time in years (2 years)
250,000 = 225,000 * (1 + r/4)^(4*2)
Simplifying:
250,000/225,000 = (1 + r/4)^(8)
5/4 = (1 + r/4)^(8)
Taking the 8th root of both sides:
(5/4)^(1/8) = 1 + r/4
Simplifying:
1.012101272 = 1 + r/4
Subtracting 1 from both sides:
r/4 = 0.012101272
Multiplying both sides by 4:
r = 0.048405089
The equivalent interest rate on the 2-year payment plan is approximately 4.84%.
Therefore, the equivalent interest rate on the 2-year payment plan is 4.84%.