In: Finance
Appalachian Bank offers you a $135,000, 9-year term loan at 7.5 percent annual interest. What will your annual loan payment be? Semi-annual compounding.
We need to calculate the annual loan payment on the loan. We can do this using the PMT formula on excel as shown below.
Loan Amount = PV | -1,35,000 |
Annualized Rate | 7.50% |
Tenor | 9 Years |
Future Value | 0 |
Annuity Type | Ordinary Annuity |
Howver, we need to note that, compounding is being done on a semi-annual basis (6 months). Hence, we need to adjust the number of periods and the rate used to calculate the payment.
Rate to be used = r = Annual Rate / (12 / compounding in months)
Rate to be used = r = 7.5% / 2 = 3.75%
Number of periods = Years x (12 / compounding in months)
Number of periods = 9 x 2 = 18
Now, the PMT formula should be implemented as given below:
Adjusted Rate | 3.75% |
Adjusted No. of Periods | 18 |
Semi Annual Payment | PMT(3.75%,18,-135000,0,0) |
Semi Annual Payment = $ 10,448.54
Annual Payment = Semi Annual Payment x 2
Annual Payment = $ 20,897.09 ......Answer