Question

Alan is taking out a $15,000 loan from a bank to renovate his house. The bank is charging him an interest rate of 4% p.a., monthly compounding. The loan has to be repaid in 60 equal monthly instalments, with the first payment due a month from now).

1. (a) (2 points) How much is each monthly payment?

2. (b) (3 points) For the 24th payment (i.e., the payment that he will make 2 years

   from now), what is the ratio between (i) the portion of that payment that represents interest and (ii) the portion of that payment that represents principal repayment?

Answer 1

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	$             15,000.00
Int rate per Month	0.3333%
No. of Months	60

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 15000 / PVAF (0.0033 , 60)
= $ 15000 / 54.2991
= $ 276.25

Amortization schedule for first 24 Months:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$             15,000.00	$            276.25	$                  50.00	$                226.25	$               14,773.75
2	$             14,773.75	$            276.25	$                  49.25	$                227.00	$               14,546.75
3	$             14,546.75	$            276.25	$                  48.49	$                227.76	$               14,318.99
4	$             14,318.99	$            276.25	$                  47.73	$                228.52	$               14,090.47
5	$             14,090.47	$            276.25	$                  46.97	$                229.28	$               13,861.19
6	$             13,861.19	$            276.25	$                  46.20	$                230.04	$               13,631.15
7	$             13,631.15	$            276.25	$                  45.44	$                230.81	$               13,400.34
8	$             13,400.34	$            276.25	$                  44.67	$                231.58	$               13,168.76
9	$             13,168.76	$            276.25	$                  43.90	$                232.35	$               12,936.41
10	$             12,936.41	$            276.25	$                  43.12	$                233.13	$               12,703.28
11	$             12,703.28	$            276.25	$                  42.34	$                233.90	$               12,469.38
12	$             12,469.38	$            276.25	$                  41.56	$                234.68	$               12,234.69
13	$             12,234.69	$            276.25	$                  40.78	$                235.47	$               11,999.23
14	$             11,999.23	$            276.25	$                  40.00	$                236.25	$               11,762.98
15	$             11,762.98	$            276.25	$                  39.21	$                237.04	$               11,525.94
16	$             11,525.94	$            276.25	$                  38.42	$                237.83	$               11,288.11
17	$             11,288.11	$            276.25	$                  37.63	$                238.62	$               11,049.49
18	$             11,049.49	$            276.25	$                  36.83	$                239.42	$               10,810.08
19	$             10,810.08	$            276.25	$                  36.03	$                240.21	$               10,569.86
20	$             10,569.86	$            276.25	$                  35.23	$                241.01	$               10,328.85
21	$             10,328.85	$            276.25	$                  34.43	$                241.82	$               10,087.03
22	$             10,087.03	$            276.25	$                  33.62	$                242.62	$                 9,844.40
23	$               9,844.40	$            276.25	$                  32.81	$                243.43	$                 9,600.97
24	$               9,600.97	$            276.25	$                  32.00	$                244.24	$                 9,356.73

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

% of Payment towards Int = Int / EMI

= $ 32 / $ 276.25

= 0.1158 I.e 11.58%

% of Payment towards Principal = Principal Reapyment / EMI

= $ 244.24 / 276.25

= 0.8842 I.e 88.42%