How much must Ms. Brown set aside today in a bank to achieve a $10,000 balance in 2 years, given a 10% interest rate with monthly compounding?

To determine how much Ms. Brown must set aside today to achieve a future balance of $10,000 in 2 years at a 10% interest rate with monthly compounding, we use the formula for present value under compound interest.

The formula for present value (PV) when future value (FV), interest rate (r), and number of periods (n) are known is:

[ PV = \frac{FV}{(1 + \frac{r}{m})^{n \cdot m}} ]

Where:

• FV is the future value, which is $10,000 in this case.

• r is the annual interest rate (10% or 0.10).

• m is the number of compounding periods per year (12 months).

• n is the number of years (2).

Substituting the values into the formula:

[ PV = \frac{10,000}{(1 + \frac{0.10}{12})^{2 \cdot 12}} ]

Calculating the periodic interest rate:

[ \frac{0.10}{12} = 0.0083333 ]

Now calculate the total number of compounding periods:

[ 2 \cdot 12