Answer:
To calculate the amount needed to save for retirement, we can use the future value formula for compound interest:
\[FV = PV \times (1 + r)^n\]
Where:
FV = Future value (desired amount for retirement)
PV = Present value (amount to be invested)
r = Interest rate per compounding period
n = Number of compounding periods
In this case, we want to find the present value (PV) that needs to be invested to reach $700,000 in 20 years, with an interest rate of 9% per year.
Plugging in the values into the formula:
\[700,000 = PV \times (1 + 0.09)^{20}\]
To solve for PV, we can rearrange the formula:
\[PV = \frac{700,000}{(1 + 0.09)^{20}}\]
Calculating this expression:
PV = 700,000 / (1.09)^20 ≈ $170,258.76
So, approximately $170,258.76 needs to be invested to reach $700,000 for retirement in 20 years with an interest rate of 9%.
