A washing machine selling for 𝑅𝑀 600 cash was purchased through an instalment
plan in which a 15 % down payment was made. The buyer had to make 25 weekly
payments of 𝑅𝑀 22 each to settle the balance. Calculate the:
i. instalment price
ii. total interest charged
iii. flat rate that was charged
iv. APR that was charged
remaining balance (present value of the loan) = .85(600) = 510
let the weekly rate be i, expressed as a decimal
then
22(1 - (1+i)^-25)/i = 510
very nasty equation to solve, we need some "tools", let's use Wolfram
https://www.wolframalpha.com/input/?i=solve+22%281+-+%281%2Bx%29%5E-25%29%2Fx+%3D+510
(I had to change the i to x, it assumed i=√-1 )
found a weekly rate of .00589465 or a rate of .30652 or a whopping annual rate of 30.7%
check:
22(1 - 1.00589465^-25)/.00589465) = 510.00
Don't know exactly what you mean by "flat rate" and APR, since I don't know the laws in
your country. The above is done using actuarial math
Your dealer probably used the following argument:
Dealer: "after downpayment of 15% you still owe 600-90 = RM 510
you made 25 payments of 22 , that is, you paid RM 550
So "we charge you only" RM 40 in interest, not bad since that is
40/510 or .07843 or 7.843%
You say: Ahh, but that is only for 25 weeks or only about 1/2 year.
Dealer says: ok, you are right, so it would be about 15.7% per year, which is still
better than a credit card, right?
What do you think?
To calculate the various values, let's break down the given information step by step.
i. Instalment Price:
The instalment price is the total amount paid for the washing machine, including both the down payment and the weekly payments.
Given:
Cash price of the washing machine = RM 600
Down payment made = 15% of the cash price
First, find the amount of the down payment:
15% of RM 600 = 0.15 * 600 = RM 90
Now, subtract the down payment from the cash price to find the remaining balance:
Cash price - Down payment = RM 600 - RM 90 = RM 510
Finally, add the remaining balance to the total amount paid in weekly installments (25 payments of RM 22 each):
Instalment Price = RM 510 + (25 * RM 22) = RM 510 + RM 550 = RM 1060
Therefore, the instalment price is RM 1060.
ii. Total Interest Charged:
To find the total interest charged, subtract the cash price from the instalment price:
Total Interest Charged = Instalment Price - Cash Price
Total Interest Charged = RM 1060 - RM 600 = RM 460
Therefore, the total interest charged is RM 460.
iii. Flat Rate Charged:
The flat rate is the percentage of the cash price that represents the total interest charged. To find the flat rate, divide the total interest charged by the cash price and multiply by 100:
Flat Rate Charged = (Total Interest Charged / Cash Price) * 100
Flat Rate Charged = (RM 460 / RM 600) * 100 ≈ 76.67%
Therefore, the flat rate charged is approximately 76.67%.
iv. APR Charged:
APR (Annual Percentage Rate) is the annual interest rate charged on the loan. Since the instalment period is given in weeks, we need to convert it to the annual period.
Given:
Weekly Payments = RM 22
Number of weekly payments = 25
To calculate the APR, we need to find the total amount paid over one year (52 weeks) and compare it to the cash price.
First, find the total amount paid over one year:
Total Amount Paid over one year = Weekly Payments * Number of weekly payments
Total Amount Paid over one year = RM 22 * 25 = RM 550
Then, calculate the APR by dividing the total amount paid over one year by the cash price and multiplying by 100:
APR = (Total Amount Paid over one year / Cash Price) * 100
APR = (RM 550 / RM 600) * 100 ≈ 91.67%
Therefore, the APR charged is approximately 91.67%.
To calculate the required values, we will follow these steps:
i. To find the installment price:
- Start with the cash price of the washing machine: RM 600
- Subtract the down payment, which is 15% of RM 600: 0.15 * 600 = RM 90
- The installment price is the remaining balance after the down payment: RM 600 - RM 90 = RM 510
ii. To calculate the total interest charged:
- Multiply the weekly payment amount by the number of payments: RM 22 * 25 = RM 550
- The total interest charged is the difference between the installment price and the total payments made: RM 550 - RM 510 = RM 40
iii. To determine the flat rate charged:
- Divide the total interest charged by the installment price: RM 40 / RM 510
- Convert the result to a percentage: (40 / 510) * 100 = 7.8%
iv. To calculate the APR:
- The Annual Percentage Rate (APR) is a bit more complex as it involves compounding and the duration of the loan.
- Assuming the payments are made weekly, there are 52 weeks in a year.
- Convert the weekly interest rate from step iii to a yearly rate: 7.8% * 52 = 405.6%
Keep in mind that the APR calculation is simplified and may not consider any additional fees or charges.