Question

Abdalla took a $12,000 loan at an interest of 12 % compounded bi-monthly. He needs to pay it over 5 years.

Construct the amortization schedule on this loan for the first three bi-monthly payments.

Answer 1

Given:

Loan amount = $ 12,000

Tenure = 5 years

Interest rate = 12%

Coupounidng is done bi-monthly, Hence number of periods = 5 * 12 * 2 = 120

Interest rate per period = 12% / (12 * 2) = 12% / 24 = 0.5%

The Payment every period can be caculated using the PMT formula is Excel as follows:

PMT(rate,nper,pv)

where rate is the Interest rate per period = 0.5%

nper is the number of periods = 120

pv is the present value of the loan = 12000

PMT(0.5%,120,-12000) = 133.22

Hence, Payment per period = $ 133.22

Ammortization schedule for first 3 bi-monthly Payments:

Period	Balance (Start)	Periodic Payment	Interest	Principal	Balance (End)
1	$ 12,000	$133.22	$60.00	$73.22	$11,926.78
2	$11,926.78	$133.22	$59.63	$73.59	$11,853.18
3	$11,853.18	$133.22	$59.27	$73.96	$11,779.23

Balance start refers to the Balance at the starting of the period. Initially it is the value of the loan and from the next period, it is equal to the ending Balance of the previous period

Periodic payment is calculated above and remains the same for all the periods

Interest = Interest per period * Beginning balance

For Period 1, Interest = 0.5% * 12,000 = 60,

For Period 2, Interest = 0.5% * 11926.78 = 59.63

For Period 3, Interest = 0.5% * 11853.18 = 59.27

Principal = Periodic Payment - Interest

For Period 1, Principal = $ 133.22 - 60 = $ 73.22

For Period 2, Principal = $ 133.22 - 59.63 = $ 73.59

For Period 3, Principal = $ 133.22 - 59.27 = $ 73.96

Ending Balance = Beginning Balance - Principal

For Period 1, Ending balance = 12000 - 73.22 = 11,926.78

For Period 2, Ending balance = 11,926.78 - 73.59 = 11,853.18

For Period 1, Ending balance = 11,853.18- 73.96 = 11,779.23

Alternatively Payment per period can also be calculated using the below formula:

where PMT is the periodic payment,

P is the Loan amount = 12000

r is the interest rate per period = 0.5%

n is the number of periods = 120