Need Help Solving Retiement Finance Math Question!!!!!!!!!!!!

[youngmula]

Some people look forward to retiring from work by the age 65. Compare the amounts at age 65 that would result from making annual deposit of $1000 starting at age 20, or from making annual deposits of $3000 starting from age 50, to an RRSP that earns 6% interest per annum, compounded monthly. What are the totals of the deposits in each situation? What are the final amounts for both situations and state which one is more profitable.

So far by using the formula fv=[(1+i)^n-1]/ i

The RRSP balance from age 20 to age 65 is $212 743.51
The RRSP balance from age 50 to age 65 is $ 69 827.91

I'm having trouble explaining the totals of the deposits. Pls could some show me how to do it . Thanx

 

[DrPhil]

Some people look forward to retiring from work by the age 65. Compare the amounts at age 65 that would result from making annual deposit of $1000 starting at age 20, or from making annual deposits of $3000 starting from age 50, to an RRSP that earns 6% interest per annum, compounded monthly. What are the totals of the deposits in each situation? What are the final amounts for both situations and state which one is more profitable.

So far by using the formula fv=[(1+i)^n-1]/ i

The RRSP balance from age 20 to age 65 is $212 743.51
The RRSP balance from age 50 to age 65 is $ 69 827.91

I'm having trouble explaining the totals of the deposits. Pls could some show me how to do it . Thanx

The total of the deposits is the SAME for the two cases:
(45 years)($1000/year) = (15 years)($3000/year) = $45 000

At the beginning of the first year, you make a deposit D (either $1000 or $3000).

At the end of each year you multiply the previous balance by 1.061678, AND you add another amount D (except for the very last year). Is that what your formula does?

 

[JeffM]

Some people look forward to retiring from work by the age 65. Compare the amounts at age 65 that would result from making annual deposit of $1000 starting at age 20, or from making annual deposits of $3000 starting from age 50, to an RRSP that earns 6% interest per annum, compounded monthly. What are the totals of the deposits in each situation? What are the final amounts for both situations and state which one is more profitable.

So far by using the formula fv=[(1+i)^n-1]/ i

The RRSP balance from age 20 to age 65 is $212 743.51
The RRSP balance from age 50 to age 65 is $ 69 827.91

I'm having trouble explaining the totals of the deposits. Pls could some show me how to do it . Thanx

Two points.

First, I get answers that are roughly comparable to yours. The reason that the totals are so different is that the longer series is benefiting from interest accumulation over a much longer time. Very roughly, the total of $3000 contributed at ages 20, 21, and 22 is earning compounded interest for over 40 years whereas the $3000 contributed at age 50 is only earning interest for at most 15 years.

Second, I am not getting the same totals as you are. The reason probably is that you have not described the problem completely so I have had to guess. Are the deposits made at the start of the year, at the end of the year, or in installments during the year? If in installments, how many and when? Four equal quarterly installment made at the end of each quarter gives a different answer than will twelve equal monthly installments made at the start of each month.

 

[Xire]

OPs answers look correct to me... of course, I did just register to get help on similar problems, so maybe I'm just wrong as well. But this is what I did to get his answers on the calculator;

Age 20: 1000((((1.06)^45)-1)/0.06) = $212,743.51
Age 50: 3000((((1.06)^15)-1)/0.06) = $69,827.91

 

[JeffM]

OPs answers look correct to me... of course, I did just register to get help on similar problems, so maybe I'm just wrong as well. But this is what I did to get his answers on the calculator;

Age 20: 1000((((1.06)^45)-1)/0.06) = $212,743.51
Age 50: 3000((((1.06)^15)-1)/0.06) = $69,827.91

As I explained in my original post, you will get roughly similar but not exactly identical answers depending on whether deposits are made monthly, quarterly, or annually, and on whether deposits are made at the start or end of periods. You have to be very careful to pose such questions carefully to get exact answers.