What formulas do you have for the annuity?
What you can do is either re-arrange to solve for n or use a numerical scheme if you can't re-arrange n by itself on only one side of the equation.
Jane Doe is 25 years old and starting next year wants to
save and invest in order to ensure an annual income of $100kin each of the 20 years after she retires, till she is 85. She willretire at 65.
She expects to earn 10% interest till retirement and 5%interest in the years after retirement.
How much must she save each year from now till retirementstarting next year?
This part is easy; PVA with pmt=100k, t=20, r=5% --> ~$1,246,200
The second part: As it turned out, Jane spent the next 5 years on the beach inBarcelona. She is 30 now and has $4,000 in the bank. Howmuch does she need to save each year, starting next year?All other data unchanged.
What should be my thought process behind this? I know the future value when she's 65 should be $1,246,200, interest should be 10%, and there's 35 more years.
1. Jane wants $1000 per year after retirement at 5% interest, so she would want to know the present value of annuity(pva) at the point of retirement,
#p=>pension & r=>interest rate & n=> no. of years
putting the values,
Now that jane has to have $ 1246221 at retirement, it becomes a future value problem now:
# c=cash payments to bank
since jane wants to have 1246221 as future value at retirement,
so jane would need to save at least and invest it, to fulfill her plans...
2. I guess the $4000 accumulated by jane would get compounded annually and contribute in making the $ 1246221, which she requires at the point of retirement.
now we will again calculate c (cash payments to bank) like we did before but take into account the $ 1246221
solving for c we get
note that in the second case jane's savings or cash payment to bank has increased from $2815.72 to $4183.49. This is because, Jane would have made more by saving what she had for 5 years than she had earned at barcelona.If she had saved $ 2815.72 per year for 5 years, her account would have gone to or
So jane made a terrible decision and I have tried to make approximations upto 2 decimal places
please correct me if i am wrong.