Question

A.

After graduating from college with a bachelor of business administration, you begin an ambitious plan to retire in 24.00 years. To build up your retirement fund, you will make quarterly payments into a mutual fund that on average will pay 11.32% APR compounded quarterly. To get you started, a relative gives you a graduation gift of $3,296.00.

Once retired, you plan on moving your investment to a money market fund that will pay 4.32% APR with monthly compounding. As a young retiree, you believe you will live for 30.00 more years and will make monthly withdrawals of $9,245.00. (YOUR WITHDRAWALS ARE AT THE BEGINNING OF THE MONTH!!!!) To meet your retirement needs, what quarterly payment should you make?

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b.

A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,731,200.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 3.00 years before the first payment. At that point, the friend will make quarterly payments for 18.00 years. The deal calls for a 6.48% APR “loan” rate with quarterly compounding. What quarterly payment will the friend make on the loan?

Answer 1

A	B	C	D	E	F	G	H	I
2		A)
3		The quarterly payment should be such that the future value of deposits at the time of retirement equals
4		the present value of the withdrawals at the time of retirement.
5
6		Present value of the withdrawals at the time of retirement	=9245+9245*(P/A,4.32%/12,30*12-1)
7			$1,870,445.91	=9245+9245*PV(4.32%/12,30*12-1,-1,0)
8
9		Assuming the quarterly payment is A then
10		Future value of deposits at the time of retirement	=3296*(F/P,11.32%/4,24*4)+A*(F/A,11.32%/4,24*4)
11
12		(F/P,11.32%/4,24*4)	14.57	=(1+11.32%/4)^(24*4)
13		(F/A,11.32%/4,24*4)	479.56	=FV(11.32%/4,24*4,-1,0)
14
15		Future value of deposits at the time of retirement	=3296*(F/P,11.32%/4,24*4)+A*(F/A,11.32%/4,24*4)
16			=3296*14.57+A*479.56
17			=48,027.66+A*479.56
18
19		Since FV of deposits and PV of withdrawal at the time of retirement should be equal, therefore
20		$1,870,445.91=48,027.66+A*479.56
21		Solving the above equation,
22		A	$3,800.20	=(D7-3296*D12)/D13
23
24		Hence quarterly deposit should be	$3,800.20
25