to supplement your retirement, you estimate that you need to accumulate
$360,000 exactly 38 years from today. you plan to make equal, end-of-year deposits into an account paying  11 % annual interest.
a.  how large must the annual deposits be to create the
$360, 000 fund by the end of 38 years?
b.  if you can afford to deposit only $590 per year into theaccount, how much will you have accumulated in 38 years?

a) $765.13 b) $277,601.23

Step-by-step explanation:

a) The problem is an example of an ordinary annuity (deposits at the end of the period).

The future value of this type of annuity is:

Clearing the annual deposit A

The deposit needed to have $360,000 in 38 years is $765.13

b) We can use the same formula to compute the FV of a known deposit:

With annual deposits of $590 you will have at 38 years an ammount of $277,601.23

step-by-step explanation:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional