Question

You need a 30-year, fixed-rate mortgage to buy a new home for $265,000. Your mortgage bank will lend you the money at an APR of 5.6 percent for this 360-month loan. However, you can only afford monthly payments of $1,050, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.

    

How large will this balloon payment have to be for you to keep your monthly payments at $1,050? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Answer 1

This question requires application of time value of money concept.

Loan Amount = PV of monthly payments + PV (balloon payment)

In order to calculate the PV of monthly payment, we need to calculate the value of monthly pay,ment of $1,050 at rate of 5.6% (on monthly basis).

PV of annuity is mathematically represented as:

P = $1050, r = 5.6%/12 = 0.467%, n = 360

PV (monthly payment) = 1050 * 174.1921 = $182,901.66

PV (balloon payment) = 265,000 - 182,901.66 = $82,098.34

We need to compound this PV of balloon payment to find its value when it is to be paid.

FV = PV * (1 + r)ⁿ

FV = 82098.34 * (1 + 0.00467)³⁶⁰

FV = 82098.34 * 5.3446

FV = $438,785.16 -----> Value of balloon payment when made at end of 360 months. Answer