Final answer:
The future value of the money in the savings account, compounded monthly at a 3% annual interest rate, is approximately $425.10 in two months.
Step-by-step explanation:
The formula for the future value of an amount compounded continuously is given by:
FV = PV * (1 + r/n)nt
Where:
- FV is the future value
- PV is the present value
- r is the interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, the present value (PV) is $420, the interest rate (r) is 3% (0.03), the number of times interest is compounded per year (n) is 12 (since it is compounded monthly), and the number of years (t) is 2/12 (since we want to find the value in two months).
Substituting these values into the formula, we have:
FV = 420 * (1 + 0.03/12)2/12
Using a calculator, the future value (FV) is approximately $425.10.