Question

You have decided to purchase a small tract of land for building a new home on the outskirts of town. You have some money available but need a loan of $18,000 to make the purchase. The land will be owner-financed over 4 years with end-of-year payments. The interest rate is 9%.

For each of the payback methods given, determine the present worth of the loan payments made by the borrower, using TVOM rates of 5%, 9%, and 13%

Method 1: Pay the accumulated interest at the end of each interest period and repay the principal at the end of the loan period.

Method 2: Make equal principal payments, plus interest on the unpaid balance at the end of the period.

Method 3: Make equal end-of-period payments.

Method 4: Make a single payment of principal and interest at the end of the loan period.

Method 5: Pay $3,000 principal at the end of the first year, then $4,000, $5,000, and $6,000 at the end of years 2, 3, 4, plus the accumulated interest at the end of each interest period.

Answer 1

Method 1)

Interest = 18000*9% =1620

$1620 per year will be paid for first 3 years and 19620 will be paid at the end of 4th year.

Presents worth of loan

Year	Value	5% pvf	PV @ 5%	9% pvf	PV @9%	13%	PV @ 13%
1	1620	0.9524	1542.89	0.9174	1486.19	0.8850	1433.70
2	1620	0.9070	1469.34	0.8417	1363.55	0.7831	1268.62
3	1620	0.8638	1399.36	0.7722	1250.96	0.6931	1122.82
4	19620	0.8227	16141.37	0.7084	13898.81	0.6133	12032.95
Total	24480		20552.96		17999.51		15858.09

Method 2) equal principal per year plus interest on unpaid balance:

First year=4500+ 18000*9%= 6120

Second Year = 4500+ 13500*9% =5715

Third year = 4500+ 9000*9%= 5310

Fourty year = 4500 +4500*9%=4905

Year	Amount	PV @ 5%	PV @ 9%	PV @13%
1	6120	5828.57	5614.68	5415.93
2	5715	5183.67	4810.2	4475.68
3	5310	4586.98	4100.29	3680.10
4	4905	4035.36	3474.83	3008.33
		15599.22	18000	16580.4

Method 3)

Equal payment at every year

Installment Amount = 18000/pvifa of 9%

= 18000/3.2397

= $5556

Present Value of Money = Installment per year* pvifa @x%

Present value of money @5% = 5556*pvifa@5%

= 5556* 3.54595

= $19701.30

Present value of Money @9% =5556*3.23972 =$18000

Present Value of Money @13%= 5556*2.9745 = $16526

Method 4) Make a Single Payment

Cumulative Interest including principal = Principal(1+r)^n

Here, r = interest rate and n= years

Amount = 18000(1+0.09)^4

= 18000*1.41158

= $25408.47

Calculation of present value,

Here, Present Value of Money = Amount *pvf@x%

@5% = 25408.47*0.8227 = $20903.61

@9% = 25408.47*0.7084 =$18000

@13% = 25408.47*0.6133 = $15583.49

Method 5)

Year	Amount	PV @5%	PV@9%	PV@13%
1	4620	4400	4238.53	4088.50
2	5350	4852.61	4502.99	4189.83
3	5990	5174.39	4625.38	4151.37
4	6540	5380.47	4633.10	4011.10
		19807.47	18000	16440.81