Question

Problem 7 (14 pts.)

Tompkins Company bought some property this year and signed a $350,000, 4%, 5-year note payable to obtain it.

Tompkins’ monthly payment is $5,500. Complete the table below for the first three payments.

                                      Interest Expense         Reduction of principal       Remaining principal

             Month 1

    

               Month 2

               Month 3

Problem 8 (16 pts.)

Use the following table to assist you in calculating your answers. Show your work.
			2%	4%	8%	16%
PV of $1		10 periods	0.820	0.676	0.463	0.227
		20 periods	0.673	0.456	0.215	0.051
PV of an annuity of $1		10 periods	8.983	8.111	6.710	4.833
		20 periods	16.351	13.590	9.818	5.929
FV of $1		10 periods	1.219	1.480	2.159	4.411
		20 periods	1.486	2.191	4.661	19.461
FV of an annuity of $1		10 periods	10.950	12.006	14.487	21.321
		20 periods	24.300	29.778	45.762	115.380

1. Larry Keeler deposits $1,200 into his Roth IRA account every three months. What will be the balance in his account at the end of 5 years if the fund earns interest at an annual rate of 8%, compounded quarterly?

2. EFL Corporation is offering a $100,000 college scholarship that will be awarded to an 8^th grader when they graduate from high school in five years. How much should EFL invest today at 8%, compounded semiannually, in order to have the $100,000 available five years from now?

3. Howard Kelly inherited $40,000 and invested it in a fund that pays 4% interest. How much will he have in his account in 20 years?  

4. Jack Costanza wants to remove $10,000 every year from an investment account to help his children pay for their college costs over the next 10 years. If the fund pays 8% interest, how much would he have to invest today?

Answer 1

Problem 7 : Repayment schedule for 1st year

Months	Project M	Interest	Installment	Reduction in Principal	Remaining Principal
	A	B	C	D	E
		A*4%/12	Given	C-B	A-D
1	350,000.00	1,166.67	5,500.00	4,333.33	345,666.67
2	345,666.67	1,152.22	5,500.00	4,347.78	341,318.89
3	341,318.89	1,137.73	5,500.00	4,362.27	336,956.62
4	336,956.62	1,123.19	5,500.00	4,376.81	332,579.81
5	332,579.81	1,108.60	5,500.00	4,391.40	328,188.41
6	328,188.41	1,093.96	5,500.00	4,406.04	323,782.37
7	323,782.37	1,079.27	5,500.00	4,420.73	319,361.64
8	319,361.64	1,064.54	5,500.00	4,435.46	314,926.18
9	314,926.18	1,049.75	5,500.00	4,450.25	310,475.94
10	310,475.94	1,034.92	5,500.00	4,465.08	306,010.86
11	306,010.86	1,020.04	5,500.00	4,479.96	301,530.89
12	301,530.89	1,005.10	5,500.00	4,494.90	297,035.99

Question 8 :

	Annuity Value
A)		PN=d((1+r/k)^Nk−1)/(r/k)
	Here	PN is the balance in the account after N years.
		d is the regular deposit (the amount you deposit each year, each month, etc.)= 1200
		r is the annual interest rate in decimal form.= 8 % p.a
		k is the number of compounding periods in one year. = 4
		N is the number of years = 5
		PN= 1200((1+0.08/4)^5*4−1)/(0.08/4) = $ 29,156.84
	Or	FV of an Anuuity $ 1, 20 years, 2% = 24.3 *1200= $29160
B)	Present value of Investment =
	Here	Future Value = $ 1,00,000
		n = No of years = 5*2 = 10 years
		I = Rate of Interest semiannully = 8%/2 = 4%
		Future Value of $1 , 10 periods, 4 % = 1.480
		PV	100000/1.480 = $ 67567.57
		Interest	32,432.43
C)	Future value of Investment =
	Here	Present Value = $ 40,000
		n = No of years = 20 years
		I = Rate of Interest = 4%
		PV of Annuity, 20years , 4% = 13.590
		Value of Investment after 20 years = 40,000*13.590 = $ 543,600
D)	Present value of Investment =
	Here	Future Value = $ 10,000
		n = No of years = 10 years
		I = Rate of Interest = 8%
		PV of Annuity $ 1, 10 years, 8% = 4.833
		Value of Investment = 10000*4.833 = $ 48,330