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How much money needs to be invested now to obtain $5000 in 10 years if the interest rate in a CD (certificate of deposit) is 2.25% compounded monthly? Round to the nearest cent.

User JeffZheng
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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.

User WesleyE
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