Question

1. If we know that a bond has a cost of $500 and that it will return $800 in 12 years, what is the interest rate, assuming that it is compounded annually?

2. XYZ corporation earnings per share were $2.78, and its growth rate was 9.5% per year for 10 years. At that rate, how long would it take for its earnings per share to double?

3. If you deposit $500 at the end of each year for 10 years and earn 8% per year, how much would you have at the end of 10 years?

4. If you invest $3,000 per year beginning at age 20, and continue doing this until you are 75 years old, and earn 9% interest, compounded annually, how much would you have at age 75?

5. If you must have $25,000 in 10 years, but you can contribute only $2,000 per year, what rate of return must you earn to reach your goal?

Answer 1

1

Investment		500.00
Principal repayment		800
Total return	FV	800.00
Number of periods		12
Realised return=	(FV/Investment)^(1/N) -1
Realised return=	(800/500)^(1/12)-1
	3.99%

Rate of return is 3.99%

2

It takes around 7.64 years to double as shown in below calculation using trial and error:

Present value of money:	=	FV/ (1+r) ^N
Future value	FV=	$                   5.56
Rate of interest	r=	9.5%
Number of years	N=	7.64
Present value	=	5.56/ (1+0.095)^7.64
	=	$                   2.78

3

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                  500.00
rate of interest per period	r=
Rate of interest per year		8.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.08*12/12	8.0000%
Number of periods
Number of years		10
Number of payments in a year		1
Total number of periods	n=	10
FV of annuity	=	500* [ (1+0.08)^10 -1]/0.08
FV of annuity	=	7,243.28

Balance in 10 years is $7,243.28

4

FV of annuity due	=	(1+r) * P * [ (1+r)^n -1 ]/r
Periodic payment	P=	$              3,000.00
Rate of interest per period	r=
Rate of interest per year		9.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.09*12/12	9.0000%
Number of periods	n=
Number of years		56.00
Number of payments in a year		1
Total number of payments	n=	56
FV of annuity due	=	(1+0.09) * 3000 [ (1+0.09)^ 56 -1] /0.09
	=	4,494,615.19

Balance by age 75 is $4,494,615.19

5

Required rate of return is 4.87% at which future value is $25,000.

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	25,000.00
Rate per period	r
Annual interest		4.87%
Number of interest payments per year		1
Interest rate per period		0.0487/1=
Interest rate per period		4.870%
Number of periods	n
Number of years		10
Periods per year		1
number of periods		10
Period payment	=	25000*0.0487/ [(1+0.0487)^10 -1]
	=	1,999.71

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