Question

Suppose that you want to have a $90,000 retirement fund after 35 years. How much will you need to deposit now if you can obtain an APR of 12%, compounded daily? Assume that no additional deposits are to be made to the account.

A. Present value calculation

B. Future value calculation

C. Annuity calculation

D. Compound interest calculation

Answer 1

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.