Final answer:
To have $5000 in 10 years with a CD at a 2.25% interest rate compounded monthly, approximately $3993.47 must be invested today.
Step-by-step explanation:
To determine how much money needs to be invested now to obtain $5000 in 10 years with an interest rate of 2.25% compounded monthly, we can use the formula for the present value of a lump sum:
PV = FV / (1 + r/n)nt
Where:
- PV is the present value or the initial amount to invest.
- FV is the future value or the amount we want after 10 years, which is $5000.
- r is the annual interest rate (expressed as a decimal), so 2.25% becomes 0.0225.
- n is the number of times the interest is compounded per year, which is 12 for monthly compounding.
- t is the number of years the money is invested, which is 10 in this case.
Using these values in our formula, we get:
PV = 5000 / (1 + 0.0225/12)12*10
PV = 5000 / (1 + 0.001875)120
PV = 5000 / (1.001875)120
PV ≈ 5000 / 1.252177 ≈ $3993.47
Therefore, you would need to invest approximately $3993.47 today in a CD at a 2.25% interest rate compounded monthly to have $5000 in 10 years. This amount is rounded to the nearest cent.