Question

1. If you put up $27,000 today in exchange for a 7.75 percent, 11-year annuity, what will the annual cash flow be?

2. You want to have $63,000 in your savings account 8 years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 7.7 percent interest, what amount must you deposit each year?

3. Prescott Bank offers you a $35,000, 8-year term loan at 10 percent annual interest. What will your annual loan payment be?

4. You want to start a business that you believe can produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $250,000. At a discount rate of 16 percent, what is this business worth today?

5. Sue just purchased an annuity that will pay $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?

6. You have been purchasing $12,000 worth of stock annually for the past eight years and now have a portfolio valued at $87,881. What is your annual rate of return?

Answer 1

1

Annual payment is:

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]
P=	Present value	27,000.00
r=	Rate of interest per period
	Rate of interest per annum	8%
	Payments per year	1.00
	Rate of interest per period	7.750%
n=	number of payments:
	Number of years	11
	Payments per year	1.00
	number of payments	11
	Annuity payment=	27000/ [ (1- (1+0.0775)^-11)/0.0775 ]
	Annuity payment=	3,736.32

2

Annuity payment=	[FV of annuity * r]/ [ ((1+r)^n -1) * (1+r)]
FV of annuity	=	63,000
rate of interest per period	r=	7.70%
Number of periods	n=	8
Annuity payment=	[ 63000*0.077]/ [ ((1+0.077)^8 -1) * (1+0.077)]
	5559.368

3

Yearly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	35,000.00
Rate of interest per period:
Annual rate of interest		10.000%
Frequency of payment	=	Once in 12 month period
Numer of payments in a year	=	12/12 =	1
Rate of interest per period	R	0.1 /1 =	10.0000%
Total number of payments:
Frequency of payment	=	Once in 12 month period
Number of years of loan repayment	=	8
Total number of payments	N	8*1 =	8
Period payment using the formula	=	[ 35000*0.1*(1+0.1)^8] / [(1+0.1 ^8 -1]
Yearly payment	=	6,560.54

4

Particulars	1	2	3
Cash flow	5600	48200	375000
Discount factor	0.862069	0.743163	0.6406577
Present value	4,827.59	35,820.45	240,246.63
Present worth	280,894.67

5

	Present value of annuity due=	P* [ [1- (1+r)-(n-1) ]/r ] + P
P=	Periodic payment	24,000.00
r=	Rate of interest per period:
	Annual rate of interest	8.5000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.085/1=	8.500%
n=	number of payments:
	Number of years	25
	Payments per year	1
	number of payments	25
	Present value of annuity=	24000* [ [1- (1+0.085)^-(25-1)]/0.085 ] +24000
	Present value of annuity=	266,498.33

Purchase price is 266,498.33

6

At around -2.54% rate of return portfolio will reach 87,881

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	12,000
rate of interest per period	r=
Rate of interest per year		-2.5400%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		-0.0254*12/12	-2.5400%
Number of periods
Number of years		8
Number of payments in a year		1
Total number of periods	n=	8
FV of annuity	=	12000* [ (1+-0.0254)^8 -1]/-0.0254
FV of annuity	=	87,885.66