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 can deposit $11,000 on each birthday beginning with his 26th and ending with his 65th. What will the rate on the retirement account need to be for him to have $3,000,000 in it when he retires on his 65th birthday?

Answer 1

To solve this problem, we can break it down step by step and identify the values for \( N \) (number of periods), \( PMT \) (payment per period), \( i/y \) (interest rate per period), \( FV \) (future value), and \( PV \) (present value). In this scenario, we are trying to find the interest rate \( i/y \).

Given information:

• Annual Deposit (PMT): $11,000 (the amount Derek deposits each birthday)
• Total Number of Deposits (N): Since he deposits starting at age 26 up to and including age 65, that’s 40 deposits.
  • 65 - 26 + 1 = 40
• Future Value (FV): $3,000,000 (the amount he wants at retirement)
• Present Value (PV): $0 (the account starts with no initial balance)

Values to enter into the financial calculator:

• \( N \) = 40 (total number of deposits)
• \( PMT \) = 11,000 (the amount deposited each year)
• \( FV \) = 3,000,000 (what he wants to have at the end)
• \( PV \) = 0 (the present value of the account before any deposits)
• \( i/y \) = ? (the interest rate that we need to find)

Calculation:

To find the interest rate, you'll input these values into the financial calculator and solve for \( i/y \).

Here's how you set it up in a financial calculator:

1. Enter \( N = 40 \)
2. Enter \( PMT = 11,000 \)
3. Enter \( FV = 3,000,000 \)
4. Enter \( PV = 0 \)
5. Solve for \( i/y \) (the annual interest rate)

Once you input these values correctly and run the calculation, the calculator will give you the annual interest rate needed for Derek to reach his goal of $3,000,000 by the time he is 65.