What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question below.

Derek will deposit $2,761.00 per year for 12.00 years into an account that earns 6.00%, The first deposit is made next year. He has $11,247.00 in his account today. How much will be in the account 44.00 years from today?

1 answer

To determine how much will be in the account 44 years from today, you need to consider both the future value of the annual deposits and the future value of the current account balance.

Step 1: Calculate the Future Value of the Annual Deposits

Given:

  • PMT (annual deposit) = $2,761.00
  • N (number of deposits) = 12 years
  • i/y (interest rate) = 6.00% or 0.06
  • FV (future value of the deposits)

The future value of the annuity (deposits) after 12 years can be calculated using the FV formula for an annuity:

\[ FV = PMT \times \left( \frac{(1 + i)^{N} - 1}{i} \right) \]

Step 2: Calculate the Future Value of the Current Account Balance

Given:

  • PV (present value today) = $11,247.00
  • N (number of years to grow) = 44 years (12 years of deposits + 32 years of growth afterwards)
  • i/y (interest rate) = 6.00% or 0.06
  • FV (future value of the current account)

The future value of the current account balance can be calculated using the FV formula for a lump sum:

\[ FV = PV \times (1 + i)^{N} \]

Putting it all together

  1. Future Value of the Annity (Deposits):

    • N = 12
    • PMT = 2,761
    • i/y = 0.06
  2. Future Value of Current Account:

    • N for this account is 44 years
    • PV = 11,247
    • i/y = 0.06

Finance Calculator Entry

  1. For Future Value of Annual Deposits:

    • N = 12
    • PMT = 2761
    • i/y = 6
    • FV = (calculate this value)
  2. For Future Value of Current Account:

    • N = 44
    • PV = 11247
    • i/y = 6
    • FV = (calculate this value)

Final Calculation:

After calculating both future values, you will add them together to get the total amount in the account 44 years from today.

In summary, on your calculator, you would input the following:

For the annuity:

  • N = 12
  • PMT = 2761
  • i/y = 6
  • Solve for FV

For the lump sum:

  • N = 44
  • PV = 11247
  • i/y = 6
  • Solve for FV

Add both future values together for the final amount in the account.