To determine how much will be in the account 33 years from today, we can break this problem down into two parts:
- Calculate the future value of Derek's deposits at the end of 9 years.
- Determine the future value of that amount when it is allowed to grow for an additional period until 33 years from today.
Step 1: Calculate the future value of the deposits
Derek will deposit $5,238 annually for 9 years, but his first deposit is made 7 years from today. This means that for the first 9 deposits, the first deposit is made at the end of the 7th year.
To calculate the future value (FV) of these deposits at the end of the 9 years using a finance calculator, we need to take into account that he will make the first deposit 7 years from today and the last one 15 years from today (since he makes 9 deposits).
For the 9 deposits:
- N (number of deposits): 9
- PMT (annual deposit): 5,238
- i/y (interest rate): 7% or 0.07
- PV (present value): 0 (since it's an investment starting from 0)
- FV: This is what we want to find out at the end of the 9th deposit (or end of 15 years from today, which is 33 - 18).
Input for Step 1:
- N = 9
- PMT = 5,238
- i/y = 7
- PV = 0
- FV = ?
Calculation for Step 1:
- Calculate FV for these annual deposits at the end of 9 years, yielding FV at year 15.
Step 2: Calculate the future value of that amount at year 33.
The amount in the account at the end of year 15 (which is the future value we found in Step 1) will now grow for another 18 years (from year 15 to year 33).
- N: 18 (years from year 15 to year 33)
- PV: (the FV from Step 1, which is calculated in Step 1)
- i/y: 7% (the same interest rate)
- PMT: 0 (he is not making additional deposits at this time)
Input for Step 2:
- N = 18
- PMT = 0
- i/y = 7
- PV = (Result from Step 1)
- FV = ?
By following these steps and using the finance calculator, you'll find the amount in the account 33 years from today.