+118 You decide to take advantage of the store’s payment plan. The Chromebook costs $499.99. The payment plan’s terms are as follows: 18 equal monthly payments, 6% interest p.a., compounded monthly. What is the total cost that you will end up paying for the Chromebook?
+1234 To calculate the total cost of the Chromebook with the payment plan, we can leverage the concept of compound interest. Here's how:
Monthly Interest Rate:
The annual interest rate is 6%. Since the payments are compounded monthly, we need to convert this to a monthly rate.
Monthly interest rate = Annual interest rate / Number of compounding periods per year
Monthly interest rate = 6% / 12 months = 0.5% per month (converted to a decimal)
Number of Payments:
The payment plan involves 18 equal monthly payments.
Cost of Chromebook:
The Chromebook's cost is $499.99.
Formula for Monthly Payment:
We can use the following formula to calculate the monthly payment amount:
Monthly payment = Loan amount * (Monthly interest rate / (1 - (1 + Monthly interest rate)^(-Number of payments)))
Calculation:
Plug in the values:
Loan amount = $499.99
Monthly interest rate = 0.005 (converted from 0.5%)
Number of payments = 18
Calculate the monthly payment:
Monthly payment = $499.99 * (0.005 / (1 - (1 + 0.005)^(-18)))
Monthly payment = $28.61 (rounded to two decimal places)
Total Cost:
Since there are 18 equal payments of $28.61 each, the total cost will be:
Total cost = Number of payments * Monthly payment
Total cost = 18 payments * $28.61/payment
Total cost = $514.98 (rounded to two decimal places)
Therefore, by taking the payment plan with monthly compounding interest, you will end up paying a total of $514.98 for the $499.99 Chromebook.
