Question

James wants to buy a flat screen television for his new apartment. 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 interest using a 90-day promissory note. James also visited the PayDay Loan store to compare the cost of borrowing. The manager told James that he could borrow $500 at 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. He wondered how much it would cost to pay the loan back in 12 weeks so he could compare the cost to the banks lending rate. He recognized that 12 weeks is a few days less than 90 days.

1) Calculate the total cost (principal plus interest) for the 90-day promissory note from the bank.
2) How much will James pay if he gets the loan from the PayDay Loan store and pays the balance back in two weeks?
3]How much will it cost if James gets his loan from the PayDay Loan store and pays it back in 12 weeks (nearly 90 days)?

Answer 1

The total cost for the 90-day promissory note from the bank can be calculated using the principal and interest. The total cost for the loan from the PayDay Loan store with a 2-week repayment can also be calculated using the principal and interest. Finally, the total cost for the loan from the PayDay Loan store with a 12-week repayment can be calculated by adding the interest for the first 2 weeks and the additional interest for the next 10 weeks.

Step-by-step explanation:

Let's calculate the total cost for both the 90-day promissory note from the bank and the loan from the PayDay Loan store:

1) Total cost for the 90-day promissory note from the bank:

Principal: $500 (loan amount)

Interest: $500 * 12% (annual interest rate) * 90/365 (pro-rated for 90 days)

Total cost: Principal + Interest

2) Total cost for the loan from the PayDay Loan store with 2-week repayment:

Principal: $500 (loan amount)

Interest: $500 * 12% (annual interest rate) * 2/52 (pro-rated for 2 weeks)

Total cost: Principal + Interest

3) Total cost for the loan from the PayDay Loan store with 12-week repayment:

Principal: $500 (loan amount)

Interest for the first 2 weeks: $500 * 12% (annual interest rate) * 2/52

Additional interest for the next 10 weeks: ($500 + Interest for the first 2 weeks) * 16% (additional weekly interest rate) * 10

Total cost: Principal + Interest for the first 2 weeks + Additional interest for the next 10 weeks