The big idea: Each deposit grows for a different number of periods. The earliest deposits have the most time to earn interest.
| Deposit | Time available to grow |
|---|---|
| First deposit | longest |
| Middle deposit | medium |
| Last deposit | shortest |
Not all deposits grow equally long: This is why an annuity is not just payment × number of periods.
Future value: The future value of a savings annuity is the total value at the end after all the deposits and their growth are combined.
Small-scale example
Three deposits of $100 are made yearly into an account earning 10% per year. Which deposit contributes the most at the end?
Step by step
- The first deposit has the most time to grow.
- The last deposit has the least time to grow.
Final answer
The first deposit contributes the most.
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Main approach: In IB, these questions are often handled using TVM or annuity functions on the calculator, but you should still understand what the variables mean.
| Variable | Meaning |
|---|---|
| PMT | regular deposit |
| N | number of periods |
| I% | interest rate |
| FV | future value |
Savings annuity sign sense: For calculator workflows, deposits may be entered with one sign and the final amount with the opposite sign, depending on convention.
More than one way to save: IB may ask which savings plan gives the larger final value. You compare the final accumulated amounts, not just the deposit sizes.
Reasoning example
Which might produce more after many years: smaller monthly deposits at a better rate, or larger deposits at a weaker rate?
Step by step
- You cannot decide from one feature only.
- You must compare the final values after the same time period.
Final answer
Calculate both plans and compare the future values.