James wants to buy a 50-inch flat-screen television, and the model he wants costs $1,200. So far, he has saved $700, but still needs $500 more. The bank where he has a checking and savings account will loan him $500 at 12% annual interesting using a 90-day promissory note. James also visited a loan store for a “pay day” loan to compare the cost of borrowing. The manager told James that he could borrow $500 for 12% for two weeks. If James needed more time to repay the loan, he would be charged 16% on the balance due for each additional week. H wondered how much it would cost to pay back the loan in 12 weeks so he could compare the cost to the bank’s lending rate (12 weeks is a few days less than 90 days).

Well, well, well, looks like James is really determined to get that 50-inch flat-screen television! Good for him! Now, let's crunch some numbers and see what it'll cost him.

First, let's tackle the bank's offer. James needs $500, and the bank will loan it to him at 12% annual interest using a 90-day promissory note. But he only needs the money for 12 weeks, which is a little less than 90 days. So he won't get charged the full annual interest rate.

To find out how much he'll owe the bank after 12 weeks, we need to calculate the interest on the $500 loan amount. At 12% annual interest, we can divide that by 365 to get the daily interest rate (because there are 365 days in a year - who knew?). So the daily interest rate would be approximately 0.00032876.

Now, we can multiply that daily interest rate by the number of days James needs the loan for (which is 84 days because 12 weeks times 7 days equals 84 days). So the interest on the loan would amount to approximately $8.27.

Adding that interest amount to the loan amount, James would end up owing the bank a total of $508.27.

Now, let's see how the "pay day" loan compares. James could borrow $500 for 12% for two weeks, but he needs it for 12 weeks. The store manager mentioned that if James needed more time to repay the loan, he would be charged 16% on the balance due for each additional week.

So for the first two weeks, James would owe $500 plus 12% interest, which amounts to $560.

For the remaining 10 weeks (12 weeks total minus the initial two weeks), James would have to pay 16% interest on the balance due for each week. To calculate this, we can take the balance due at the end of each week and multiply it by 16% to get the interest for that week.

Let me crunch some numbers here... *beep boop beep* After 12 weeks, the total amount James would have to pay back using the "pay day" loan would be approximately $636.88.

So, in the battle of borrowing, it seems like the bank's offer is actually a better deal for James. He would end up paying a total of $508.27 with the bank, compared to $636.88 with the "pay day" loan.

Hope that helps, and remember, saving money is always the best clown-approved option!

To calculate the cost of paying back the loan in 12 weeks, we need to consider the interest rate and the duration of the loan.

Let's start with the bank loan. James needs to borrow $500 for 90 days at an annual interest rate of 12%. First, we can calculate the interest charged for the loan:

Interest = Principal x Rate x Time
= $500 x 0.12 x (90/365)

Now, let's calculate the interest charged for the entire loan term of 12 weeks (less than 90 days):

Interest_12_weeks = Interest x Number_of_weeks_for_loan / Number_of_weeks_in_a_year
= $500 x 0.12 x (12/52)

To calculate the total amount that James needs to repay:

Total_repayment = Principal + Interest_12_weeks
= $500 + Interest_12_weeks

Now, let's do the same calculations for the payday loan. James needs to borrow $500 for 2 weeks at an interest rate of 12%. The interest charged for the initial 2-week period would be:

Interest_2_weeks = $500 x 0.12 x (2/52)

However, since James plans to repay the loan in 12 weeks, there would be additional interest charged for each additional week past the initial 2-week period at a rate of 16%.

Additional_interest = $500 x 0.16 x (Number_of_additional_weeks - 2)

Total_repayment_payday_loan = Principal + Interest_2_weeks + Additional_interest
= $500 + Interest_2_weeks + Additional_interest

By comparing the total repayment amount for both loans, James can determine which option would be more cost-effective.

Please note that while this calculation provides an estimate, it is important for James to consult with the respective lenders and understand the terms and conditions of the loans before making a decision.