Question

Loan amortization schedule   

Joan Messineo borrowed ​$40,000 at a 4​% annual rate of interest to be repaid over 3 years. The loan is amortized into three​ equal, annual,​ end-of-year payments

a. Calculate the​ annual, end-of-year loan payment.

b.  Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

a.  The amount of the​ equal, annual,​ end-of-year loan payment is ____. [Round to the nearest cent.]

Answer 1

Annual Instalment:
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

Part A:

Particulars	Amount
Loan Amount	$             40,000.00
Int rate per Anum	4.0000%
No. of Years	3

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 40000 / PVAF (0.04 , 3)
= $ 40000 / 2.7751
= $ 14413.94

Part B:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$             40,000.00	$       14,413.94	$            1,600.00	$          12,813.94	$               27,186.06
2	$             27,186.06	$       14,413.94	$            1,087.44	$          13,326.50	$               13,859.56
3	$             13,859.56	$       14,413.94	$               554.38	$          13,859.56	$                         0.00

Opening Balance = Previous month closing balance
EMI = Instalment calculated
Int = Opening Balance * Int Rate
Principal repay = Instalment - Int
Closing Balance = Opening balance - Principal Repay

Part C:

In every year some portion will be adjusted toPrincipal. Which will reduce the opening balance on which int shall be calculated. Hence as it approaches towards maturity, Int will be reduced.