Question

Set up an amortization schedule a $30,000 loan to be repaid in equal installments at the next 3 years. The interest rate is 8% compounded semiannually

a) amortize loan with fixed principal payment

b) amortized loan with fixed payment

Answer 1

Step-1:Calculation of effective annual interest rate
Effective annual interest rate	=	Effective annual interest rate
(1+i)^n	=	(1+i)^n
(1+0.04)^2	=	(1+i)^1
1.0816	=	1+i
0.0816	=	i
So,
Effective annual rate	=	8.16%
Step-2:Amortization Schedule
a)
Year end	Beginning Loan	Interest	Prinicipal repaid	Total payment	Ending Loan
	a	b=a*8.16%	c	d=b+c	e=a-c
1	30,000.00	2,448.00	10,000.00	12,448.00	20,000.00
2	20,000.00	1,632.00	10,000.00	11,632.00	10,000.00
3	10,000.00	816.00	10,000.00	10,816.00	0.00
Total		4,896.00	30,000.00	34,896.00
b)
Year end	Beginning Loan	Interest	Payment	Prinicipal repaid	Ending Loan
	a	b=a*8.16%	c	d=c-b	e=a-d
1	30,000.00	2,448.00	11,674.63	9,226.63	20,773.37
2	20,773.37	1,695.11	11,674.63	9,979.52	10,793.85
3	10,793.85	880.78	11,674.63	10,793.85	0.00
Total		5,023.89	35,023.89	30,000.00
Working:
Equal annual payment	=-pmt(rate,nper,pv,fv)
	= $ 11,674.63
Where,
rate	=	8.16%
nper	=	3
pv	=	$       30,000
fv	=	0