Question

To pay off a loan of $8,900 due in five years, a person will make a deposit at the end of each year into an account paying 9.3% interest compounded annually. Determine the size of the deposit rounded up to the nearest half-dollar and construct a table that shows the size of each deposit, the amount of interest, and the balance after each payment.

Answer 1

a) Size of payment		=	Loan amount	/	Present value of annuity of 1
		=	$ 8,900.00	/	3.8595618
		=	$ 2,305.96
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.093)^-5)/0.093		i	=	9.30%
		=	3.8595618		n	=	5
b) Amortization Schedule:
Year	Beginning Loan	Interest Expense	Annual payment	Reduction of principal	Ending Loan amount
	a	b=a*9.30%	c	d=c-b	e=a-d
1	$ 8,900.00	$ 827.70	$ 2,305.96	$ 1,478.26	$ 7,421.74
2	$ 7,421.74	$ 690.22	$ 2,305.96	$ 1,615.74	$ 5,806.00
3	$ 5,806.00	$ 539.96	$ 2,305.96	$ 1,766.00	$ 4,040.00
4	$ 4,040.00	$ 375.72	$ 2,305.96	$ 1,930.24	$ 2,109.75
5	$ 2,109.75	$ 196.21	$ 2,305.96	$ 2,109.75	$        -0.00