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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?

 Mar 27, 2024
 #1
avatar+1121 
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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.

 Mar 30, 2024
 #2
avatar+359 
0

Using an interest payment calculator, each payment is 32.51, so the total cost is 18*32.51 = 585.18.

 Mar 30, 2024

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