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

Question

Derek will deposit $3,997.00 per year for 28.00 years into an account that earns 10.00%, The first deposit is made next year. How much will be in the account 38.00 years from today?

Answer 1

To solve for the future value of an annuity (the total amount in the account in the future after making annual deposits), you can use a financial calculator by entering the following values for N, PMT, i/y, FV, and PV.

Here’s how to break it down for Derek’s situation:

1. N (number of periods): This will be the total number of years until the final future value is calculated. Derek will make deposits for 28 years, but since you're calculating how much will be in the account 38 years from today, you need to account for those additional 10 years where the money will continue to grow after the last deposit. So, \(N = 28\) (during deposit years) and then additional 10 years for growth without deposits, giving you a total of \(N = 38\).

2. PMT (payment per period): This is the amount Derek deposits each year. \(PMT = 3997\).

3. i/y (interest rate per period): This is the annual interest rate as a decimal. \(i/y = 10.00\).

4. FV (future value): This is what we're trying to calculate, so you can leave this blank initially while you perform the calculation.

5. PV (present value): Since Derek starts with nothing in the account, \(PV = 0\).

Now that we have our values for the first part (the accumulation during the deposit period), we can calculate the future value after 28 years:

1. Input the values:
   • N = 28
   • PMT = 3997
   • i/y = 10
   • PV = 0
   • Compute FV (this gives the future value of the annuity after 28 years).

After calculating FV after the initial 28 deposits, you have the total in the account at that time. This will be labeled as FV1.

Now you need to consider that this total \(FV1\) will continue to grow at the 10% interest for an additional 10 years:

So you will use those results as follows in your calculator:

1. Input the values for future value from step 1:
   • N = 10 (for the 10 years of growth)
   • PMT = 0 (no more deposits)
   • i/y = 10
   • PV = FV1 (the result from the first calculation)
   • Compute FV (this gives you the total amount in the account after 38 years).

Overall, to summarize:

1. First calculation (28 years): N=28, PMT=3997, i/y=10, PV=0; Compute FV1.
2. Second calculation (after additional 10 years): N=10, PMT=0, i/y=10, PV=FV1; Compute FV for total after 38 years.

You can use any financial calculator or spreadsheet to handle these calculations accordingly.