Question

Suppose you borrowed $50,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

Answer 1

Annual Instalment:
Annual 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	$             50,000.00
Int rate per Anum	8.5000%
No. of Years	5

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 50000 / PVAF (0.085 , 5)
= $ 50000 / 3.9406
= $ 12688.29
Loan AortizationSchedule:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$             50,000.00	$       12,688.29	$            4,250.00	$            8,438.29	$               41,561.71
2	$             41,561.71	$       12,688.29	$            3,532.75	$            9,155.54	$               32,406.17
3	$             32,406.17	$       12,688.29	$            2,754.52	$            9,933.76	$               22,472.41
4	$             22,472.41	$       12,688.29	$            1,910.15	$          10,778.13	$               11,694.27
5	$             11,694.27	$       12,688.29	$               994.01	$          11,694.27	$                        -0.00

Amount reduced in forst Year is amount adjusted towards Principal repayment. I.e $ 8438.29

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