# Saving/Income problem

#### filipchaush2000

##### New member
Been having some problems with this one, hope that someone would have the time to type out a step by step result thank you upfront. Heres the question:

Melissa wants to save money to meet two objectives. First she would like to be able to retire 20 years from now and have a retirement income of $30,000 per year for 30 years. Second she would like to purchase a car 5 years from now at an estimated cost f$20,000. She can afford to save only$6,000 per year for the first 10 years. Melissa expects to earn 8% per year from investments over the next 50 years. What must be her minimum annual savings be from years 11 through 20 to meet her objectives? #### lev888 ##### Senior Member hope that someone would have the time to type out a step by step result Wrong forum. Please read posting guidelines. #### Subhotosh Khan ##### Super Moderator Staff member Been having some problems with this one, hope that someone would have the time to type out a step by step result thank you upfront. Heres the question: Melissa wants to save money to meet two objectives. First she would like to be able to retire 20 years from now and have a retirement income of$30,000 per year for 30 years. Second she would like to purchase a car 5 years from now at an estimated cost f $20,000. She can afford to save only$6,000 per year for the first 10 years. Melissa expects to earn 8% per year from investments over the next 50 years. What must be her minimum annual savings be from years 11 through 20 to meet her objectives?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### JeffM

##### Elite Member
Well the first thing I would do is to figure out what is going to happen over the first five years? How much must she save each year to buy the car? Suppose she saves just enough to buy the car? How much would have to be saved in succeeding years to meet the retirement goal? Can it be done?

#### jonah2.0

##### Full Member
Beer soaked ramblings follow.
Been having some problems with this one, hope that someone would have the time to type out a step by step result thank you upfront. Heres the question:

Melissa wants to save money to meet two objectives. First she would like to be able to retire 20 years from now and have a retirement income of $30,000 per year for 30 years. Second she would like to purchase a car 5 years from now at an estimated cost f$20,000. She can afford to save only\$6,000 per year for the first 10 years. Melissa expects to earn 8% per year from investments over the next 50 years. What must be her minimum annual savings be from years 11 through 20 to meet her objectives?
The key phrases for your problem are equations of value and comparison date.
Convenient comparison dates are the present (now or time 0 or beginning of 1st year), end of 5 years, end of 20 years. The problem's solution will also vary depending on when the annual savings deposit are to be made and when the retirement income are to be drawn, i.e., beginning of the year (annuity due) or end of the year (ordinary annuity).

Note also that the most efficient way to solve an annuity problem is to make a time diagram, determine the type of annuity, and then apply the proper formula(s).
Draw up a line graph (or a time diagram) from 0 to 50.
Mark point 0 as the beginning of the 1st year, mark point 1 as the end of the 1st year (aka the beginning of the 2nd year), and so on and so forth until the end of the 50th year.
The 1st savings deposit is either at point 0 or at point 1 depending upon clarification from you.
Same deal with car purchase time and retirement income withdrawals.

The quesion is: What have you tried so far?

Note: Man I miss Denis and his tips/hints (along with his occasional caffeine induced long funny rants). It saddens me that a lot of his posts have been obliterated.

#### JeffM

##### Elite Member
Beer soaked ramblings follow.

The key phrases for your problem are equations of value and comparison date.
Convenient comparison dates are the present (now or time 0 or beginning of 1st year), end of 5 years, end of 20 years. The problem's solution will also vary depending on when the annual savings deposit are to be made and when the retirement income are to be drawn, i.e., beginning of the year (annuity due) or end of the year (ordinary annuity).

Note also that the most efficient way to solve an annuity problem is to make a time diagram, determine the type of annuity, and then apply the proper formula(s).
Draw up a line graph (or a time diagram) from 0 to 50.
Mark point 0 as the beginning of the 1st year, mark point 1 as the end of the 1st year (aka the beginning of the 2nd year), and so on and so forth until the end of the 50th year.
The 1st savings deposit is either at point 0 or at point 1 depending upon clarification from you.
Same deal with car purchase time and retirement income withdrawals.

The quesion is: What have you tried so far?

Note: Man I miss Denis and his tips/hints (along with his occasional caffeine induced long funny rants). It saddens me that a lot of his posts have been obliterated.
Yep denis would have said “write a looper.”