Question

Alan wants to buy a new TV at $500, but he is missing $15. Jessica promised...

  1. Alan wants to buy a new TV at $500, but he is missing $15. Jessica promised that if he gave her $100 this month, she would pay him back $125 the next month. After a month, Alan receives his money back, but the TV price has increased by 6%.
    1. What is the nominal interest rate on this loan?
    2. What is the real interest rate on this loan?

Hint: you can use a CPI of 100 for the first month as the base.

  1. Can Alan buy his TV in the end?
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Homework Answers

Answer #1

Nominal intrest on the loan = (total repayment - initial loan / initial loan)*100

=(125-100 /100)*100 = 25%

Real interest rate on loan = nominal interest rate - rate of inflation

rate of inflation = (CPI current moneth- CPI last month / CPI last month)*100

= (106-100 /100)*100 = 6%

Thus, real interest rate = 25 - 6 = 19%

Total money with Alan after a month = 485 - 100 + 125 = 510

Cost of TV after a month = 1.06*500 = 530

Thus, Alan can not buy the TV in the end

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