# Inflation and Loan

Problem 3

Which do you prefer: a bank account that pays 5% per year (EAR) for three years or

a. An account that pays 2 every six months for three years?

b. An account that pays 7 every 18 months for three years?

c. An account that pays per month for three years?

If you deposit $1 into a bank account that pays 5% per year for 3 years you will have after 3 years.

a. If the account pays per 6 months then you will have after 3 years, so you prefer every 6 months.

b. If the account pays per 18 months then you will have after 3 years, so you prefer 5% per year.

c. If the account pays per month then you will have after 3 years, so you prefer every month.

Problem 6 Your bank account pays

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d. Suppose you are willing to continue making monthly payments of $1402, and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing?

a. First we calculate the outstanding balance of the mortgage. There are 25 × 12 = 300 months remaining on the loan, so the timeline is as follows. Timeline #1: 0 | 1 | 2 | | | | 300 | | | | | | | | | | | | | | | | | | | | | | | | 1,402 | 1,402 | | | | 1,402 | To determine the outstanding balance we discount at the original rate, i.e., Next we calculate the loan payment on the new mortgage. Timeline #2: 0 | 1 | 2 | | | | 360 | | | | | | | | | | | | | | | | | | | | | | | 154,286.22 | –C | –C | | | | –C | The discount rate on the new loan is the new loan rate: Using the formula for the loan payment:

b. c. (You can use trial and error or the annuity calculator to solve for N.) d. (Note: results may differ slightly due to rounding.)

Problem 26 In 1975, interest rates were 7.85% and the rate of inflation was 12.3% in the United States. What was the real interest rate in 1975? How would the purchasing power of your savings have changed over the year?

The purchasing power of your savings declined by 3.96% over the