at giant tv sales, you can chose between 2 payments options for a new tv. 1st option is 2 pay $2399.99. 2nd option is to pay a $399.99 downpayment plus $2200.00 after one year. if interset is 4.2% per year, compunded quarterly, wich option is a better deal
What interest rate are we talking about? They have given you two fixed amounts. Nothing was said about a loan. Better provide more detailed information here.
Is there a 3rd plan, where you finance the $2200?
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To determine which payment option is a better deal, we need to compare the total amount paid for each option.
Option 1: Paying $2399.99 upfront.
Option 2: Paying a $399.99 downpayment plus $2200.00 after one year.
Let's calculate the total amount for Option 1 first. Since there is no installment or interest involved, the total amount paid will be $2399.99.
For Option 2, we have two parts to consider: the downpayment and the payment after one year.
The downpayment of $399.99 is paid immediately, so we don't need to consider any interest on this amount.
For the payment after one year, we need to calculate the compounded interest. The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, the principal (P) is $2200.00, the annual interest rate (r) is 4.2% (0.042 as a decimal), compounded quarterly (n = 4), and the time (t) is 1 year.
Using the formula, we can calculate the future value of the $2200.00 after one year:
A = 2200(1 + 0.042/4)^(4*1)
A ≈ 2200(1.0105)^4
A ≈ 2345.85
So, after one year, the payment of $2200.00 will grow to approximately $2345.85.
Now, let's calculate the total payment for Option 2:
Total payment = Downpayment + Payment after one year
Total payment = $399.99 + $2345.85
Total payment ≈ $2745.84
Therefore, the total amount paid for Option 2 is approximately $2745.84.
Comparing the total payments for both options:
Option 1: $2399.99
Option 2: $2745.84
Considering the better deal is the one with the lower total amount paid, Option 1 is a better deal in this case.