Question

You are about to ask the bank for a loan for $ 5,000 at a compound annual interest rate of 9% with a monthly capitalization. You are asked to make five semiannual payments and that the first payment be made at the end of the first semester. For each semester, calculate the interest payment and the principal payment.

Answer 1

Loan amount =	5000
Interest rate annual is 9% compounded monthly.So monthly rate = 9%/12=	0.0075
Semiannual rate = ( (1+monthly rate)^no. of months in semiannual year) -1
((1+0.0075)^6)-1=	0.0458522351
Total semiannual periods =	5
Equal annual payments for loan formula = P* i *((1+i)^n)/((1+i)^n-1)
5000*0.0458522351*((1+0.0458522351)^5)/(((1+0.0458522351)^5)-1)
$1,141.66

So, interest and principal payment is calculated in following amortization table.

	Loan amortization table
Year	Beginning balance	Payment	Interest	Principal payment	Ending balance
			(Beg. Bal.*0.0458522351)	(Payment - interest)	(Beg. Balance - principal payment.)
1	5000.00	1141.66	229.26	912.40	4087.60
2	4087.60	1141.66	187.43	954.24	3133.36
3	3133.36	1141.66	143.67	997.99	2135.36
4	2135.36	1141.66	97.91	1043.75	1091.61
5	1091.61	1141.66	50.05	1091.61	0.00
	Total	5708.32	708.32	5000.00