To determine how much must be deposited today in an account to accumulate $50,000 in 5 years, given that the account has an APR of 6% with monthly compounding, we use the present value formula for compound interest:

$PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$

Where:

• $PV$ = present value (the amount to be deposited today)
• $FV = 50,000$ (the future value or target amount)
• $r = 0.06$ (the annual interest rate, 6% expressed as a decimal)
• $n = 12$ (the number of times the interest is compounded per year, since it's monthly)
• $t = 5$ (the number of years)

Now, let's calculate it step by step.The amount that must be deposited today is approximately $37,068.61 in order to have $50,000 in 5 years with an APR of 6% and monthly compounding.

Would you like further details on this calculation or have any questions?

Here are 5 related questions you might find interesting:

1. How would the deposit amount change if the APR was 4% instead of 6%?
2. What if the compounding was done annually instead of monthly? How would the deposit change?
3. How does the present value formula differ for continuous compounding?
4. What if you wanted $50,000 in 10 years instead of 5? How would that affect the required deposit?
5. How much interest would you earn over the 5 years with the 6% APR?

Tip: The more frequently interest is compounded, the more your investment grows due to the effects of compound interest.