You have just arranged for a $1,620,000 mortgage to finance the purchase of a large tract of land. The mortgage has an APR of 6.2 percent, and it calls for monthly payments over the next 22 years. However, the loan has an eight-year balloon payment, meaning that the loan must be paid off then.
How big will the balloon payment be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) |
| Balloon payment | $ |
Explanation:
The monthly payments with a balloon payment loan are calculated assuming a longer amortization schedule, in this case, 22 years. The payments based on a 22-year repayment schedule would be: |
| PVA = $1,620,000 = C({1 – [1 / (1 + 0.062/12)264]} / (0.062/12)) |
| C = $11,258.10 |
Now, at Time = 8, we need to find the PV of the payments which have not been made. The balloon payment will be: |
| PVA = $11,258.10({1 – [1 / (1 + 0.062/12)12(14)]} / (0.062/12)) |
| PVA = $1,262,223.38 |
| Calculator Solution: |
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. |
| Enter | 22 × 12 | 6.2% / 12 | $1,620,000 | ||||||||||||
N | I/Y | PV | PMT | FV | |||||||||||
| Solve for | $11,258.10 | ||||||||||||||
| Enter | 14 × 12 | 6.2% / 12 | $11,258.10 | ||||||||||||
N | I/Y | PV | PMT | FV | |||||||||||
| Solve for | $1,262,223.38 | ||||||||||||||