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 plans to retire on his 65th birthday. However, he plans to work part-time until he turns 75.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 75.0 when he fully retires, he will begin to make annual withdrawals of $149,308.00 from his retirement account until he turns 91.00. After this final withdrawal, he wants $1.65 million remaining in his account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 8.00% interest rate.

Answer 1

To solve this problem using a finance calculator, we need to break it down into its components: the withdrawals, the remaining balance, and the contributions. We will calculate the future value (FV) of the contributions, the withdrawals, and the amount left in the account at a certain point in time.

Here's how to set it up:

1. Determine the N (number of years), PMT (annual contribution), i/y (interest rate), FV (future value), and PV (present value) for each phase of retirement savings.

Phase 1: Contributions from age 26 to 65

• N: 65 - 26 = 39 years
• i/y: 8% (the interest rate)
• FV: This will be the amount that needs to support the withdrawals and leave a $1.65 million balance after the 16 years of withdrawals.

Phase 2: Withdrawals from age 76 to 91

• N: 91 - 76 = 15 years
• PMT: -$149,308 (withdrawal is an outflow, hence negative)
• FV: $1,650,000 (amount he wants in the account after the last withdrawal)
• i/y: 8%

First, we can find out how much the account needs to have at age 75 to achieve the desired result:

Step 1: Calculate present value needed at age 75 for these withdrawals

Using the formula for present value of an annuity (PV of withdrawals):

1. Set N = 15 (years of withdrawals)
2. Set PMT = -149,308 (annual withdrawal)
3. Set i/y = 8%
4. Set FV = 1,650,000 (amount after last withdrawal)

Using a finance calculator:

1. Calculate PV at age 75 to find out how much Derek needs in the account at that age.

Step 2: Find how much must be contributed to reach this amount (PV calculated at Step 1) at age 65.

Now, calculate the amount required at age 65 that needs to grow to the PV found in Step 1 in 10 years while earning 8% interest.

1. Set N = 10 years (from age 65 to 75).
2. Set i/y = 8% (interest rate).
3. Set FV = PV (what you found from Step 1).
4. Set PMT (this is what we are looking for, the contributions).

Using the finance calculator: Calculate the PMT which represents the annual contributions that Derek should make from age 26 to 65.

Summary of Calculations

1. Phase 2 (Calculate PV needed at age 75):

   • N: 15
   • PMT: -149,308
   • i/y: 8%
   • FV: 1,650,000
   • Calculate this PV.

2. Phase 1 (Calculate PMT based on the age 65 amount):

   • N: 10
   • i/y: 8%
   • FV: (PV from Phase 2)
   • Calculate PMT.

This two-step process will give you the annual contribution Derek needs to make from age 26 to 65.