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?

SilviaJendeukie Mar 27, 2024

#1**0 **

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.

Akhain1 Mar 30, 2024