investment

Question

at the end of each year a self employed person deposits $1500 in a retirement account that earns 10 percent annually. a How much will be in the account when the individual retires at the age of 65 if the contributions start when the person is 45 years old? b how much additional money will be in the account if the individual stops making the contribution at age 65 but deferes retirement until age 70? c how much additional money will be in the account if the individual continues making the contribution but defers retirement until age 70? d Compare the answers to b and c.  what is the effects of continuing the contributions?  how much is the difference between the two answers?

Answer 1

1500 ( 1 + 0.10 ) ^20 = 10091. 24

 

 10091.24 (1.1) ^5 = 16251.65

 

  16251.65 -10091.24 = 6160.41

Answer 2

At the end of each year a self employed person deposits $1500 in a retirement account that earns 10 percent annually.

 

a.) How much will be in the account when the individual retires at the age of 65 if the contributions start when the person is 45 years old?

 

Amount in account at end of year when age is 45 =

A(45) = $1500

A(46) = $1500(1+10%) + $1500 = $1500(1.1) + $1500

A(47) = $1500(1.1)^2 + $1500(1.1) + $1500

A(48) = $1500(1.1)^3 + $1500(1.1)^2 + $1500(1.1) + $1500

...

A(65) = $1500(1.1)^20 + ... $1500(1.1)^3 + $1500(1.1)^2 + $1500(1.1) + $1500

(1.1)A(65) = $1500(1.1)^21 + ... $1500(1.1)^4 + $1500(1.1)^3 + $1500(1.1)^2 + $1500(1.1)

 

(1.1)A(65)-A(65) = $1500(1.1)^21 - $1500 = $1500 ((1.1)^21 - 1)

A(65) = $1500 ((1.1)^21 - 1) / (1.1 - 1)

A(65) = $1500 ((1.1)^21 - 1) / (0.1)

A(65) = $15000 ((1.1)^21 - 1)

A(65) ≈ $96,003.75

 

b.) How much ADDITIONAL money will be in the account if the individual stops making the contribution at age 65 but defers retirement until age 70?

 

A(65) (1.1)^5 - A(65) = A(65) ( (1.1)^5 - 1 )

= $15000 ((1.1)^21 - 1) ((1.1)^5 - 1)

≈ $58,611.25

 

c.) How much ADDITIONAL money will be in the account if the individual continues making the contribution but defers retirement until age 70?

 

A(65) = $15000 ((1.1)^21 - 1) ≈ $96,003.75

A(70) = $15000 ((1.1)^26 - 1)

A(70) ≈ $163,772.65

 

A(70) - A(65) ≈ $67,768.90

 

d.) Compare the answers to b and c.

 

Answer to b: $58,611.25

 

Answer to c: $67,768.90

 

What is the effects of continuing the contributions?

You get more money in the account at age 70 if you continue the contributions.

 

How much is the difference between the two answers?

$9,157.65; but $7500 of that are your contributions and only $1,657.65 is interest earned.

 

Moral: Invest EARLY so time is on your side!