Question

Jenny takes out a loan of $40,000 from Westpac for her small business at 6.00% p.a. compounded monthly and promises to pay it back over two years with equal monthly payments. Six months after taking out the loan (just after the sixth payment is made), she decides to re nance her loan at a lower rate of 5.00% p.a. compounded monthly o ered by National Australia Bank for the remaining term of the loan. Assuming she can do so immediately and there are no re nancing costs or charges, what will her new monthly payments be?

Answer 1

The PV of annuity formula

PV = (C/r)/(1-(1/(1+r)^n))

where

PV = Present value of Loan Amount

C = EMI Amount

r = Rate of Interest

n = number of compounding periods

putting value - PV = $40000, r= 0.5% monthly, n= 24 months in the formula above

The EMI is equal to = $ 1772.82 rounded to 1773

Now the amortization schedule

S.No	Beginning Balanace	EMI	Interest Balance	Principal Balance	Ending Balance
1	40000	1773	200	1573	38427
2	38427	1773	192	1581	36846
3	36846	1773	184	1589	35258
4	35258	1773	176	1597	33661
5	33661	1773	168	1605	32057
6	32057	1773	160	1613	30444
7	30444	1773	152	1621	28824
8	28824	1773	144	1629	27195
9	27195	1773	136	1637	25558
10	25558	1773	128	1645	23913
11	23913	1773	120	1653	22260
12	22260	1773	111	1662	20598
13	20598	1773	103	1670	18928
14	18928	1773	95	1678	17250
15	17250	1773	86	1687	15564
16	15564	1773	78	1695	13869
17	13869	1773	69	1703	12165
18	12165	1773	61	1712	10453
19	10453	1773	52	1721	8733
20	8733	1773	44	1729	7004
21	7004	1773	35	1738	5266
22	5266	1773	26	1746	3519
23	3519	1773	18	1755	1764
24	1764	1773	9	1764	0

After 6 months from amortization table above, the loan outstanding = $30444

now the Interest rate is 5% p.a. or 0.416% monthly and tie left is 18 months, so new EMI will be

30444 = (c/.00416)/(1-(1/(1.00416)^18))

c = 1758.96 or 1759

S.No

Beginning Balanace

EMI

Interest Balance

Principal Balance

Ending Balance

7	30444	1759	127	1632	28812
8	28812	1759	120	1639	27173
9	27173	1759	113	1646	25527
10	25527	1759	106	1653	23874
11	23874	1759	99	1660	22214
12	22214	1759	92	1667	20548
13	20548	1759	85	1674	18874
14	18874	1759	79	1680	17194
15	17194	1759	72	1687	15506
16	15506	1759	65	1694	13812
17	13812	1759	57	1702	12110
18	12110	1759	50	1709	10402
19	10402	1759	43	1716	8686
20	8686	1759	36	1723	6963
21	6963	1759	29	1730	5233
22	5233	1759	22	1737	3496
23	3496	1759	15	1744	1751
24	1751	1759	7	1752	0