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Homework answers / question archive / Consider the following fixed-rate level payment mortgage: - Maturity = 20 years; amount borrowed $500,000; mortgage rate = 6% per annum a
Consider the following fixed-rate level payment mortgage: - Maturity = 20 years; amount borrowed $500,000; mortgage rate = 6% per annum a. Calculate the monthly mortgage payment. (4 points) b. Calculate i) the interest, ii) scheduled principal payment for the first month and iii) the outstanding balance of the mortgage loan at the beginning of the second month. (6 points)
EMI :
EMI or Instalment is sum of money due as one of several equal payments for loan/ Mortgage taken today, spread over an agreed period of time.
EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods
How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods
| Particulars | Amount |
| Loan Amount | $ 500,000.00 |
| Int rate per Month | 0.5000% |
| No. of Months | 240 |
EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 500000 / PVAF (0.005 , 240)
= $ 500000 / 139.5808
= $ 3582.16
Part B:
| Period | Opening Bal | EMI | Int | Principal Repay | Closing Outstanding |
| 1 | $ 500,000.00 | $ 3,582.16 | $ 2,500.00 | $ 1,082.16 | $ 498,917.84 |
| 2 | $ 498,917.84 | $ 3,582.16 | $ 2,494.59 | $ 1,087.57 | $ 497,830.28 |
Int in First payment = $ 2500
Principal in first payment = $ 1082.16
Closing balance at the begining of Second payment is $ 498917.84
Opening Balance = Previous month closing balance
EMI = Instalment calculated
Int = Opening Balance * Int Rate
Principal repay = Instalment - Int
Closing Balance = Opening balance - Principal Repay
