1. You borrow $80,000 from the bank to invest in your business. You plan to repay the loan through weekly payments of $500, with the first payment occurring one week after you receive the funds from the bank, and the final payment possibly being a partial payment. The bank charges interest at a rate of j₅₂ = 3.75% p.a.

1. Determine how long it will take you to repay the loan. Describe and apply a sanity check for the duration of the loan.
2. Determine the size of the final (partial) payment.
3. Construct an amortization table showing the last six payments, that is, five full payments and a partial payment. Ensure that you show how you got your starting value for the table. Describe and apply a sanity check to your table.
4. Immediately after your 8^th payment, the interest rate increases to j₅₂ = 3.90% p.a. Assuming that you maintain the same weekly payments of $500, determine how long does it takes you to retire your debt and the size of the final (partial) payment.

2. You are opening a savings account which pays fortnightly interest at a rate of j₂₆ = 2.3% p.a. You wish to save $55,000 for a mortgage deposit by depositing the same amount into the account at the end of each month, for 2.5 years, starting in a months time.

1. Determine the required size for the fortnightly deposit, R. Apply a sanity check.
2. Construct a sinking fund table for the last five deposits. (Ensure that you show how you obtained your starting value for the table.) Describe and apply a sanity check to your table.
3. Suppose that immediately after your 25^th deposit, the interest rate rises to j₂₆ = 2.6% p.a. Determine the size of the deposits you must make in fortnight 25 an onwards in order to still make your target of $55,000.
4. With the new interest rate j₂₆ = 2.6% p.a, construct a new sinking fund table for the last five deposits. (Ensure that you show how you obtained your starting value for the table.) Describe and apply a sanity check to your table.