Financial Decisions

Sometimes we know the present value or future value but do not know one of the variables we have previously been given as an input. For example, when we take out a loan, we may know the amount we would like to borrow, but may not know the loan payments that will be required to repay it. Or, if we make a deposit into a bank account, we may want to calculate how long it will take before the balance reaches a certain level. In such situations, we use the present and/or future values as inputs, and solve for the variable we are interested in (Berk & DeMarzo, 2010).

A balloon payment is a large lump-sum payment scheduled at the end of a series of considerably smaller periodic payments. A balloon payment may be included in the payment schedule for a loan, lease, or other stream of payments. A balloon payment mortgage is a mortgage which does not fully pay off over the term of the note, consequently leaving a balance due at maturity. The final payment is called a balloon payment because of its large size. Balloon payment mortgages are more common in commercial real estate than in residential real estate. A balloon payment mortgage may have a fixed or a floating interest rate (Balloon Payment Mortgage, 2011). For problem #34 of Chapter 4, this example has a fixed interest rate of 7%.

Question #34: You would like to buy a house and take a mortgage of 30 years at $350,000 with $50,000 as a down payment. You can afford to pay $23,500 per year. The bank has agreed to this amount each year, yet still allows you to borrow $300,000. At the end of the mortgage in 30 years, you must make a balloon payment; that is you must repay the remaining balance on the mortgage. The amount of this balloon payment will be $24,174.05.

300,000=PV (30 year annuity of C/yr evaluated at 7%)

300,000=C x 1/0.07 (1 – 1/(1.07)30)

300,000=C x 14.29(.87)

300,000=C x 12.41

C=300,000/12.41

C=24,174.05

After you have finished making payments on the mortgage for 30 years in the amount of $23,500 per year, the final payment will be $24,135.16. Balloon payments may sometimes require refinancing or repayment at the end of the period; some adjustable rate mortgages do not need to be refinanced, and the interest rate is automatically adjusted at the end of the applicable period.

Retirement savings is something we all will need to consider at some point in our lives. Just like purchasing our homes, we need to consider our future once we retire. This is what is called a Future Value of an Annuity. An annuity is used in finance theory to refer to any terminating stream of fixed payments over a specified period of time (Annuity (Finance Theory), 2011). This usage is most commonly seen in discussions of finance, usually in connection with the valuation of the stream of payments, taking into account time value of money concepts such as interest rate and future values (Annuity (Finance Theory), 2011). Examples of annuities are regular deposits to a savings account, monthly home mortgage payments and monthly insurance payments. Annuities are classified by payment dates. The