Janet Woo decided to retire to fla. in 6 years. What amount should Janet invest today so she can withdraw 50000.00 at the end of each year for 20 years after she retires? What will be the balance in the account 2 years after the last deposit. I guess i am not sure here how to figure this out here. I am using a texas instrument calculator. HELP
As DrWLS pointed out, they are sinking and not sicking :)
First do the 20 year annuity problem for present value needed when she retires.
She wants 50,000 per year for 20 years
You must have some interest rate r to do the problem.
P = 50,000 * [ 1 - (1+r)^-20 ] / r
so when you retire there is that amount P in the account
Now do the amount N needed to put in your sinking fund each year for the 6 years to have that amount P in the account at retirement
N = P * r/[ (1+r)^6 - 1 ]
one year after last deposit she will have [ P (1+r) - 50,000]
two years after last deposit she will have { [ P (1+r) - 50,000]* (1+r)} - 50,000
I think i got this one here but i had to figure this out on a time line that one was hard to do. i seem to have problems with these kinda questions
A2=25000[1 - (1.09)^-30]/0.09= $256,841.35
256,841.35=A1(1.09)^10; A1= $108,492.56
To calculate the amount Janet needs to invest today, we need to use the concept of Present Value (PV). PV is the value of a future sum of money in today's dollars, taking into account the time value of money.
In this case, we need to calculate the amount Janet should invest so that she can withdraw $50,000 at the end of each year for 20 years after she retires. We'll assume an interest rate of 'r' (which is not specified in your question).
To calculate the present value, you can use the following formula:
PV = CF * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (the amount Janet needs to invest today)
CF = Cash Flow (the amount Janet wants to withdraw each year - $50,000)
r = Interest rate (annual rate of return on her investment)
n = Number of years (20 years in this case)
Now, to calculate the balance in the account 2 years after the last deposit, we need to know the interest rate and the type of compounding (annually, semi-annually, monthly, etc.). As you haven't provided the interest rate or compounding details, it is not possible to calculate the exact balance. However, I can explain the formula to calculate the future value of an investment, and you can apply it once you have the required details.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = PV * (1 + r)^n
Where:
FV = Future Value (the balance in the account)
PV = Present Value (the initial investment amount)
r = Interest rate (annual rate of return on her investment)
n = Number of years (2 years in this case)
Make sure to convert the interest rate to a decimal and to use consistent units of time (e.g., years). Once you have these values, you can input them into your Texas Instrument calculator by using the appropriate buttons or functions to perform the calculations.
If you have more specific information regarding the interest rate and the compounding frequency, please provide that, and I can help you with the exact calculations.