Susannah purchased ski equipment for $978 using a six-month deferred payment plan. The interest rate after the introductory period is 21.45%. A down payment of $150 is required as well as a minimum monthly payment of $75. What is the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period?
A.$470.87
B.$920.87
C.$845.87
D.$487.69
My answer is $487.69
To find the balance at the beginning of the seventh month, we need to first calculate the total amount paid during the introductory period.
The introductory period is six months, and during this time, only the minimum monthly payment of $75 is made. Therefore, the total amount paid during the introductory period is 6 * $75 = $450.
Next, we need to calculate the remaining balance after the introductory period. The total purchase amount was $978, and the down payment was $150. Therefore, the remaining balance after the introductory period is $978 - $150 - $450 = $378.
Since the interest rate after the introductory period is 21.45%, we need to calculate the interest for one month. The interest for one month is $378 * (21.45%/12) = $6.53.
Finally, we add the interest to the remaining balance. The balance at the beginning of the seventh month is $378 + $6.53 = $384.53.
Therefore, the correct answer is not provided in the options.
To calculate the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period, we need to break down the payment plan and calculate the interest accumulated.
First, let's calculate the total cost of the ski equipment by subtracting the down payment from the purchase price:
Total cost = $978 - $150 = $828.
During the introductory period, no interest is applied. However, the minimum monthly payment should still be made. Since the minimum payment is $75 and the introductory period lasts for six months, the total amount paid during this period is 6 * $75 = $450.
After the introductory period ends, the interest rate of 21.45% is applied to the remaining balance, which is $828 - $450 = $378.
To calculate the interest accumulated, we multiply the remaining balance by the interest rate:
Interest accumulated = $378 * 0.2145 = $81.09.
Now, we need to add the interest accumulated to the remaining balance to find the total balance at the beginning of the seventh month:
Balance = $378 + $81.09 = $459.09.
Therefore, the correct answer is D. $487.69.
balance financed = 978-150 = 828
monthly rate = .2145/12 = .017875
balance at end of 6 month if no payment had been made
= 828(1.017875)^6
= 920.87
amount of the 6 payments at that time
= 75( 1.017875^6 - 1)/.017875
= 470.60
balance owing at that time = 920.87 - 470.60 = 450.27
None of the answers match my solution.
Answers B and C aren't even logical.
How did you get 487.69 ?