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.)
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
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