Sunk Costs NonRefundable Deposit

Question

A young couple has made a nonrefundable deposit of the first month’s rent (equal to 1,000 dollars) on a 6-month apartment lease. The next day they find a different apartment that they like just as well, but its monthly rent is only 900 dollars. They plan to be in the apartment only 6 months. Should they switch to the new apartment? What if they plan to stay 1 year? Assume an interest rate of 12%.

I do not know how to start this. Please guide me in the right direction and please do not put the answer down as I want to work out.

Answer 1

1. Suppose the couple has a bank balance of \$11000 at the beginning. Then they put down the \$1000 deposit on the first apartment, leaving \$10000.
2. Suppose they keep the first apartment. Calculate how much they will have in the bank after six months, subtracting the monthly rent costs, and adding the 2% interest payments on the bank deposits each month. Don't forget that the first month's rent is already paid.
3. Suppose they take the second apartment. Calculate how much they will have in the bank after six months, subtracting the monthly rent costs, and adding the interest payments on the total balance each month.

Compare item 2 with item 3.

Perhaps you are wondering why I assumed that they started with a balance of \$11000? But it doesn't matter; it won't affect the difference between 2 and 3. Do the calculation over assuming a starting bank balance of \$8000 and see if the difference between 2 and 3 is the same.