Question

1) Mr. Robbins what’s to retire in 30 years with a total amount of $1,000,000. If he invests $75,370 today, determine the annual percentage the investment will have to earn. Assume interest is compound annually.

_________%

2) On January 1, 2015, Roxy Company sold $7,500,000 of 5% bonds, due January 1, 2025. Interest on these bonds is paid on January 1 each year (the first interest payment will be made on January 1, 2016 and the last payment will be made on JANUARY 1, 2025). THE EFFECTIVE INTEREST RATE AT THE DATE OF THE SALE WAS 6%.

REQUIRED: What total amount was received by Roxy Company on January 1, 2015? (8 points)

$____________

Part iii (continues)

4) the Annies company owes a $250,000 debt as of November 1, 2013. Arrangements are made to pay the debt in five equal annual installments the first payment will be made on November 1, 2013.

What id the amount of each installment if the prevailing annual interest rate is 5% (4 points)

$ _________

5) . Stuart Allen realized at age 62 that he had not yet started to plan for his retirement. He plans to retire at age 72. He wants to accumulate a fund that will allow him to remove $90,000 a year, for 18 years, with the first payment starting at age 72, and the last payment at age 89. To prepare for this, Stuart plans to make annual contribution into a retirement fund that has an annual rate of return of 9% during the years of his retirement)

REQUIRED: Determine the amount of each annual contribution into the retirement fund, if the first contribution occurs on his 62nd birthday and the last contribution occurs on his 71st birthday (6 Points)

Amount of each annual contribution: $______________

Answer 1

1)

MATURITY AMOUNT	$        1,000,000
PRINCIPAL AMOUNT	$              75,370
MATURITY AMOUNT = PRINCIPAL (1+ MARKET INTEREST RATE/100)^30
1000000 = 75370 (1+ R/100)^30
1000000/75370 = (1+r/100)^30
132.8021248	(1 + r/100)^30
1.176991972	= (1+r/100)
0.176991972	= r/100
R	18%

2)
INTEREST AMOUNT RECEIVED AT YEAR END = 7,500,000 * 5% =			$            375,000
YEAR	AMOUNT RECEIVED	INTEREST RATE 6%,PV FACTOR	DISCOUNTED AMOUNT
1	$                                               375,000	0.9434	$      353,773.58
2	$                                               375,000	0.8900	$      333,748.67
3	$                                               375,000	0.8396	$      314,857.23
4	$                                               375,000	0.7921	$      297,035.12
5	$                                               375,000	0.7473	$      280,221.81
6	$                                               375,000	0.7050	$      264,360.20
7	$                                               375,000	0.6651	$      249,396.42
8	$                                               375,000	0.6274	$      235,279.64
9	$                                               375,000	0.5919	$      221,961.92
10	$                                           7,875,000	0.5584	$ 4,397,358.87
		amount received	$ 6,947,993.47

show formula in excel

2)
INTEREST AMOUNT RECEIVED AT YEAR END = 7,500,000 * 5% =			=7500000* 5%
YEAR	AMOUNT RECEIVED	INTEREST RATE 6%,PV FACTOR	DISCOUNTED AMOUNT
1	375000	=1/(1.06)^A16	=B16*C16
2	375000	=1/(1.06)^A17	=B17*C17
3	375000	=1/(1.06)^A18	=B18*C18
4	375000	=1/(1.06)^A19	=B19*C19
5	375000	=1/(1.06)^A20	=B20*C20
6	375000	=1/(1.06)^A21	=B21*C21
7	375000	=1/(1.06)^A22	=B22*C22
8	375000	=1/(1.06)^A23	=B23*C23
9	375000	=1/(1.06)^A24	=B24*C24
10	=375000+7500000	=1/(1.06)^A25	=B25*C25
		amount received	=SUM(D16:D25)

4)

Year	Payment	Principal Paid	Interest Paid	Remaining Balance
2013	$57,743.70	$45,243.70	$12,500.00	$204,756.30
2014	$57,743.70	$47,505.88	$10,237.82	$157,250.42
2015	$57,743.70	$49,881.18	$7,862.52	$107,369.24
2016	$57,743.70	$52,375.24	$5,368.46	$54,994.00
2017	$57,743.70	$54,994.00	$2,749.70	$0.00
total	$288,718.50	$250,000.00	$38,718.50

EMI = [P x R x (1+R)^N]/[(1+R)^N-1],