Final answer:
To calculate the amount needed to deposit now for a $90,000 retirement fund after 35 years with an APR of 12%, compounded daily, you need to use a present value calculation. Plugging the values into the formula, the approximate amount is $3,181.75.
Step-by-step explanation:
To calculate the amount you need to deposit now to have a $90,000 retirement fund after 35 years with an APR of 12%, compounded daily, you need to use a present value calculation.
The present value formula is given by:
PV = FV / (1 + r/n)^(n*t)
where PV is the present value, FV is the future value, r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the future value (FV) is $90,000, the annual interest rate (r) is 12% (or 0.12), the compounding frequency (n) is 365 (since it is compounded daily), and the number of years (t) is 35.
Plugging these values into the formula:
PV = 90000 / (1 + 0.12/365)^(365*35)
PV ≈ $3,181.75
Therefore, you would need to deposit approximately $3,181.75 now to have a $90,000 retirement fund after 35 years.