Question

2. Which would you rather have (i.e., which is worth more five years in the future) if the annual effective interest rate is 3.5%: a. $12 000 today, or b. Five (5) annual payments of $3,000 beginning at the end of year one.

3. You’ve purchased your first home. The property taxes on it are $3,500 per year. The mortgage stipulates that the owner must pay 1/12 of the annual taxes each month to the bank so that the taxes can be paid on April 1. Your first payment is at the end of April and the last payment is at the end of March of the following year. Assume that cost of money is 6.5% nominal annual interest, compounded monthly. a. Draw the cash flow diagram for one year. b. What is the effective annual interest rate (in %)? c. Determine how much profit (in $) the mortgage company makes each year on the owner's tax money. Profit in this case is the difference in the sum of the amount you pay and the amount paid in property taxes.

4. Joan Student is projecting that she will owe a total of $28,750 in student loans when she graduates. The loans have an annual nominal interest rate of 6.5%, compounded monthly. The entire amount must be repaid within 10 years and she will make the minimum monthly payments (120 payments). a. Draw the cash-flow diagram that describes this situation. b. What is the effective annual interest rate (in %)? c. Determine what her minimum monthly payment will be.

5. A firm purchased some equipment at a price of $150,000. The equipment resulted in an annual net savings of $6,000 per year during the 10 years it was used. At the end of 10 years, the equipment was sold for $110,000. Draw a cash-flow diagram that depicts the situation. Assuming an annual effective interest rate of 6.5%, what was the equivalent cost to the company of this transaction on the purchase date? 6. Two machines are being considered to do a certain task in a manufacturing plant. Machine A costs $240,000 new and $26,000 to operate and maintain each year. Machine B costs $320,000 new and $12,000 to operate and maintain each year. The machines are identical in all other aspects and will have no salvage value after eight (8) years. Assume an annual effective interest rate of 7.0%. Determine (by the equivalent uniform annual cost method) which alternative is least expensive.

Answer 1

2.

S.No	Opening	Interest	Principal Repayments	Closing
1	3500.00	234.40	291.67	3208.33
2	3208.33	214.87	291.67	2916.67
3	2916.67	195.33	291.67	2625.00
4	2625.00	175.80	291.67	2333.33
5	2333.33	156.27	291.67	2041.67
6	2041.67	136.73	291.67	1750.00
7	1750.00	117.20	291.67	1458.33
8	1458.33	97.67	291.67	1166.67
9	1166.67	78.13	291.67	875.00
10	875.00	58.60	291.67	583.33
11	583.33	39.07	291.67	291.67
12	291.67	19.53	291.67	0.00

Nominal Interest rate	6.50%
No.of Months Compounded	12
Payment Amount per month	291.6667
Effective Annual Interest rate	6.70%(1+Nominal Interest/number of month))^n - 1

3.

Nominal Interest rate		6.50%
No.of Months Compounded		120
Payment Amount per month		239.5833(28750/12)
Effective Annual Interest rate		6.71%

5.

Year	Savings	[email protected]%
1	6000	5633.80
2	6000	5289.96
3	6000	4967.09
4	6000	4663.94
5	6000	4379.29
6	6000	4112.00
7	6000	3861.04
8	6000	3625.39
9	6000	3404.12
10	6000	3196.36
10	110000	58599.86
Present Value		101732.85
Purchase Price		150000.00
Cost to company		$48267.15

6.

S.No	Particulars	Machine A	Machine B
1	Purchase cost($)	240000	320000
2	Operating Cost P.a	26000	12000
3	Number of years	8	8
4	Effective Annual Rate(%)	7	7
5	Present value of Annuity Factor	5.971	5.971
6	Present value of Operating cost	155253.76	71655.582
7	Total Cost(1+6)	395253.76	391655.58

Therefore Cost of Machine B is lower