What value do I put for PMT, PV, N, and i/y for the question below to solve on a finance calculator?

Question

Derek will deposit $3,859.00 per year for 14.00 years into an account that earns 6.00%. Assuming the first deposit is made 4.00 years from today, how much will be in the account 30.00 years from today?

Answer 1

To solve the given problem, we need to break it down into two parts:

1. Calculating the future value (FV) of the annuity when the deposits are made.
2. Calculating the value of that future amount at the time we want to find it (30 years from today).

Step 1: Calculate the Future Value of the Annuity

Derek will deposit $3,859.00 per year for 14 years, starting 4 years from today. The annual interest rate is 6%.

Given:

• PMT (Payment) = 3,859
• N (Number of years for the annuity payments) = 14
• i/y (Interest rate per year) = 6%
• PV (Present Value) = 0 (since we are not calculating from any initial investment)

To find the future value at the end of the 14 years (which is when the last deposit is made), use the following formula for future value of an annuity:

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

Calculating FV of Annuity:

• Compute FV for the annuity after 14 years:

1. Input values into the calculator:

   • PMT = 3,859
   • N = 14
   • i/y = 6
   • PV = 0

2. Calculate FV to find out how much will be in the account just after the last payment.

Step 2: Calculate the Future Value at Year 30

Since the last payment occurs at year 14, we need to consider how long the total amount will grow until year 30. From year 14 to year 30 is 16 years.

Repeat the calculation for the FV from year 14 to year 30

Now take the future value you calculated (let's call it \(FV_{14}\)), and treat it as the present value that will grow for another 16 years at 6% interest.

Given for this second calculation:

• PV = \( FV_{14} \) (the result from the first calculation)
• N = 16 (the number of years from the end of the annuity to year 30)
• i/y = 6%

1. Enter \( FV_{14} \) as PV, and set:

   • N = 16
   • i/y = 6
   • PMT = 0 (since there are no more payments after the annuity)

2. Calculate the final FV at Year 30.

Summary of Settings for Finance Calculator:

For the first calculation (annuity future value)

• PMT: 3,859
• N: 14
• i/y: 6
• PV: 0

For the second calculation (future value after annuity)

• PV: Result from first calculation
• N: 16
• i/y: 6
• PMT: 0

This should guide you to enter the correct values to solve the problem using a finance calculator!

Answer 2

when it says " Assuming the first deposit is made 4.00 years from today," does it change the value for N at all on the first calculation

Answer 3

Yes, the 4-year delay does affect the overall time frame for the accumulation of interest but not the value for \(N\) used in the first calculation for the annuity.

Clarification:

• The 14 years for the annuity payments remain the same: Derek will make 14 annual deposits of $3,859 starting 4 years from today.
• However, the deposits will not earn interest for the first 4 years because they are made starting from year 4.

Breakdown:

1. Annuity Deposits:

   • Derek will deposit $3,859 annually starting at year 4 for a total of 14 years.
   • This means he will make his first deposit in year 4 and his last deposit in year 17. So the calculations for the annuity using \(N = 14\) are still correct.

2. Future Value of the Annuity:

   • After calculating the future value of the annuity at year 17 (after all deposits have been made), that amount will sit in the account until year 30.
   • The total period from the time the last deposit is made (year 17) to year 30 is 13 years (not 16 years).

Revised Steps:

1. Calculate the FV of the Annuity (after 14 deposits are made):

   • PMT = 3,859
   • N = 14
   • i/y = 6%
   • PV = 0

2. After calculating the FV of the annuity at the end of 14 years (i.e., at the end of year 17), you will take the output of that calculation and apply it as the present value that accumulates interest from year 17 to year 30.

3. For the second calculation (to find the FV at year 30):

   • PV = \(FV_{14}\) (the amount from the annuity calculation)
   • N = 13 (the number of years between year 17 and year 30)
   • i/y = 6%
   • PMT = 0

This means in summary, while \(N\) for the annuity is still 14, the time from the end of the last payment to year 30 is actually 13 years of growth.

Hence:

Setting for Finance Calculator:

1. Annuity Calculation:

   • PMT: 3,859
   • N: 14
   • i/y: 6
   • PV: 0

2. Future Value Calculation from year 17 to year 30:

   • PV: Result from first calculation
   • N: 13
   • i/y: 6
   • PMT: 0

This is how to correctly analyze the entire scenario based on the information provided!