SOLUTION: 19. Karen has been depositing RM300 at the end of each month in a tax-free retirement account since she was 25. Louis, who is the same age as Karen, started depositing RM420 at the

Question 1187955: 19. Karen has been depositing RM300 at the end of each month in a tax-free retirement account since she was 25. Louis, who is the same age as Karen, started depositing RM420 at the end of each month in a tax-free retirement account when he was 30. Assuming that both accounts have been and will be earning interest at the rate of 5.4%/year compounded monthly, who will end up with the larger retirement account at the age of 60, Karen or Loius?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the calculator at https://arachnoid.com/finance/index.html tells you what the future value is, as shown below:

inputs are everything but fv.
output is fv.

the calculator tells you that the 300 a month plan gives a future value of 372,757.56 at the end of 420 months, while the 420 a month plan gives a future value of 376,577.62 at the end of 360 months.

since karen has the 300 a month plan and louis has the 420 a month plan, louis winds up with more money at the end of 30 years than karen has at the end of 35 years.

that would be your solution.

that same calculator tells you when both plans have the same future value.

the calculator says that the remaining balance for the 420 a month plan will be equal to the remaining balance for the 300 a month at the end of month 330.95 for the 420 a month plan, which corresponds to end of month 391 for the 300 a month plan.

i used excel to track the monthly remaining balances.
excel shows that the 420 a month plan overtakes the 300 a month plan at end of month 331 for the 420 a month plan, which corresponds to month 391 for the 300 a month plan.

since the 420 a month plan started 60 months later, end of month 391 for the 300 a month plan is the same time frame as end of month 331 for the 420 a month plan.

here are the significant time points for both plans.

the display shows that the 420 a month plan overtakes the 300 a month plan in month 331 for the 420 a month plan, which corresponds to month 391 for the 300 a month plan.

the column heading in the excel display mean:

nyrs = number of years
nym = number of months
rpy = interest rate per year (equal to % divided by 100).
rpm = interest rate per month
paeom = payment at the end of each month
eom = end of month
rembal = remaining balance at the end of each month.

let me know if you have any questions.

theo

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