Question

Mike Polanski is 30 years of age and his salary next year will be $40,000. Mike forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60.

  

a.	If the discount rate is 8%, what is the PV of these future salary payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Present value

$

  

b.	If Mike saves 5% of his salary each year and invests these savings at an interest rate of 8%, how much will he have saved by age 60? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Future value

$

  

c.	If Mike plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  

Present value

$

Answer 1

a

	Present value of Growing annuity =	P/(r - g) × [ 1 - [(1+g)/(1+r)]n ]
P=	Periodic payment	$                             40,000
g=	Growth rate	5%
r=	Rate of interest per period:
	Annual rate of interest	8.00000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.08/1=	8.000%
n=	number of payments:
	Number of years	30
	Payments per year	1
	number of payments	30
	Present value of annuity=	40000/(0.08 - 0.05) × [ 1 - [(1+ 0.05)/(1 + 0.08 )]^30 ]
	Present value of annuity=	760,662.53

Present value of salary is $760,662.53

b

	Future value of Growing annuity =	P/(r - g) × [ (1+r)n - (1+g)n]
P=	Periodic payment	$                                   2,000
g=	Growth rate	5%
r=	Rate of interest per period:
	Annual rate of interest	8.00000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.08/1=	8.00000%
n=	number of payments:
	Number of years	30
	Payments per year	1
	number of payments	30
	Future value of annuity=	2000/(0.08 - 0.05) × [ (1 + 0.08 )^30 - (1+ 0.05)^30 ]
	Future value of annuity=	382,714.30

Future value of savings is $382,714.30

c

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]
P=	Present value	382,714.30
r=	Rate of interest per period
	Rate of interest per annum	8.0%
	Payments per year	1.00
	Rate of interest per period	8.000%
n=	number of payments:
	Number of years	20
	Payments per year	1.00
	number of payments	20
	Annuity payment=	382714.3/ [ (1- (1+0.08)^-20)/0.08 ]
	Annuity payment=	38,980.30

Annual payment each year is $38,980.30

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