Question

You have the opportunity of purchasing a farm for $500,000. The owner will allow a $100,000 down payment with the remainder financed in one of the following ways.

1. Equal annual payments with an interest rate of 7% for 20 years.

2. Equal annual payments with an interest rate of 10% for 15 years.

3. Equal quarterly payments with interest rate of 8% for 15 years.

4. Equal principal payments each year with interest rate of 8% for 10 years.

Determine the following: a. The payments for options 1-3.

b. The total interest paid for options 1-3.

c. Principal and interest paid in each of the first 4 years for option 3 and 4. (you may not know how to do option 4).

d. Which option (1-4) would you choose? Why?

Answer 1

In order order to find equal annual payments formula

=P*r*(1+r)^n/((1+r)^n-1)

P is the loan amount to be paid=(500000-100000)=400000

r is the interest rate

n is the no of years

1.

	Annual
Loan amount	400000
Interest rate	7%
Years	20
Calculation	=400000*7%*(1+7%)^20/((1+7%)^20-1)
Answer	37757.17

2

	Annual
Loan amount	400000
Interest rate	10%
Years	15
Calculation	=400000*10%*(1+10%)^15/((1+10%)^15-1)
Answer	52589.5

3.

	Annual
Loan amount	400000
Interest rate	8%
Years	15*4=60
Calculation	=400000*8%*(1+8%)^60/((1+8%)^60-1)
Answer	11507.18 Quarterly

4 Annual equal principal payments

Loan amount - 400000

interest rate 8%

n= 10 years

so annual principal payment=400000/10=40000

Year	Principal payment (A)	Interest payment loan amount 8%	Remaining loan balance Loan amount -A	Total payment
1	40000	32000 =(400000*8%)	360000 =(400000-40000)	72000
2	40000	28800 =(360000*8%)	320000	68800
3	40000	25600=(320000*8%)	280000	65600
4	40000	22400 =(280000*8%)	240000	62400
5	40000	19200= (240000*8%)	200000	59200
6	40000	16000 =(200000*8%)	160000	56000
7	40000	12800 =(160000*8%)	120000	52800
8	40000	9600 =(120000*8%)	80000	49600
9	40000	6400 =(80000*8%)	40000	46400
10	40000	3200 =(40000*8%)	0	43200
		176000	1800000	576000

b. Interest paid for 3 options

	Option1	Option 2	Option 3
Equal payment	37,757	52,590	11,507
No of installments	20	15	60
Total amount paid (A)	755,143	788,843	690,431
Principal amount (B)	400,000	400,000	400,000
interest( A-B)	355,143	388,843	290,431

c Principal and interest paid for option 3 and 4 for first 4 years

Since option 3 is paid quarterly so no of installments =(4*4)=16 installments

Year	Quarterly payment (A)	Interest payment (B)	Principal paid (A-b)	Remaining loan balance
1	11507.18633	8,000	3,507	396,493
2	11507.18633	7,930	3,577	392,915
3	11507.18633	7,858	3,649	389,267
4	11507.18633	7,785	3,722	385,545
5	11507.18633	7,711	3,796	381,748
6	11507.18633	7,635	3,872	377,876
7	11507.18633	7,558	3,950	373,927
8	11507.18633	7,479	4,029	369,898
9	11507.18633	7,398	4,109	365,789
10	11507.18633	7,316	4,191	361,597
11	11507.18633	7,232	4,275	357,322
12	11507.18633	7,146	4,361	352,961
13	11507.18633	7,059	4,448	348,513
14	11507.18633	6,970	4,537	343,976
15	11507.18633	6,880	4,628	339,349
16	11507.18633	6,787	4,720	334,629
	Total	118,744	65,371

Option 4

Year	Principal payment (A)	Interest payment loan amount 8%	Remaining loan balance Loan amount -A	Total payment
1	40000	32000 =(400000*8%)	360000 =(400000-40000)	72000
2	40000	28800 =(360000*8%)	320000	68800
3	40000	25600=(320000*8%)	280000	65600
4	40000	22400 =(280000*8%)	240000	62400
	160000	108800

d I prefer repayment of equal principal amount as the interest paid in the option 4 is less than the interest paid in the remaining loans if we have excess cash. But if we are short of cash then we can select option 1 because it offeres lower interest rate when compared to others and tenure is also very long