Jim Hunter decided to retire to Florida in 10 years. What amount should Jim invest today so that he will be able to withdraw $25,000 at the end of each year for 30 years after he retires. Assume he can invest money at 9% interest compounded annually. (Using the Tables)
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 Jim should invest today, we can use the tables related to the present value of an ordinary annuity.
Step 1: Determine the number of periods (N) and interest rate (i).
- Jim wants to withdraw $25,000 at the end of each year for 30 years after he retires. Therefore, the number of periods (N) is 30.
- The interest rate (i) is given as 9% compounded annually. Since we are using tables, we need to convert this interest rate to its decimal equivalent, which is 0.09.
Step 2: Find the Present Value Interest Factor of an Ordinary Annuity (PVIFA).
- PVIFA is a factor that will be multiplied by the annual withdrawal amount to determine the present value.
- Look up the PVIFA in the tables for N = 30 and i = 0.09. The PVIFA value from the table is 12.486.
Step 3: Calculate the present value (P) of the annuity.
- To find the present value, divide the desired annual withdrawal amount ($25,000) by the PVIFA value (12.486).
- P = $25,000 / 12.486
- P ≈ $2,004.37
Therefore, Jim should invest approximately $2,004.37 today to be able to withdraw $25,000 at the end of each year for 30 years after he retires, assuming a 9% interest rate compounded annually.
50,000
Pt = $25000/yr * 30rs = $750,000 = Amt.
in the account after 10 yrs.
Pt = Po(1+r)^n.
r = 9%/100% = 0.09 = APR expressed as a decimal.
n=1 comp./yr * 10yrs = 10 Compounding periods.
Po(1.09)^10 = 750,000.
Po = 750000 / (1.09)^10 = $316,808.11.
= Initial deposit.