Find how much to deposit today to cover a multi-year scholarship payout
PV converts a stream of equal future payments into the single amount, deposited today and left to earn interest, that would fund every one of them.
Task:
You manage the scholarship endowment for a small college's engineering department. Three named funds each pay a fixed amount to a recipient every year for a set number of years, and each fund earns its own annual interest rate while the money sits invested. In E2, work out how much needs to be deposited into the fund today so it fully covers its payouts, using PV, then copy down through E4. In E5, total the three deposits, so the department knows how much it needs to raise before any of the funds can open.
Learning Objectives:
- Use PV to convert a stream of equal future payments into a single amount needed today
- Enter a payment as a negative number when it represents money paid out rather than received
- See why discounting future payments gives a smaller number than simply multiplying payment by number of periods
Solve without hints for +5 XP
Interactive Spreadsheet
The data in this exercise
This is the grid you start with. Cell references in the task — B6, C2 — point at the row numbers and column letters below.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Scholarship Fund | Annual Payout | Years | Rate | Deposit Needed Today |
| 2 | Chen Family Scholarship | 5000 | 4 | 0.04 | |
| 3 | Whitfield Memorial Award | 3000 | 6 | 0.035 | |
| 4 | Ortiz Engineering Grant | 8000 | 3 | 0.045 | |
| 5 | Total endowment needed |
What this exercise teaches (contains the answer)
PV(D2,C2,-B2) treats each year's $5,000 payout as money leaving the fund, which is why B2 has to go in negative — a positive payment would tell PV the fund is receiving $5,000 a year rather than handing it out, and the deposit required would come back negative instead of positive. Discounting four years of $5,000 payouts back to today at 4% lands at $18,149.48, well under the $20,000 you'd get by just multiplying payout by years, because a dollar the fund hands out in year four is worth less today than a dollar it hands out next year, and PV accounts for that where a flat multiplication doesn't. The same gap shows up for the other two funds: Whitfield's $3,000-a-year, six-year award needs $15,985.66 rather than $18,000, and Ortiz's $8,000-a-year, three-year grant needs $21,991.71 rather than $24,000. SUM(E2:E4) then adds the three already-discounted deposits into the $56,126.85 the department needs to raise in total — not the same figure you'd get by discounting the three payouts as one combined stream, since each fund keeps its own rate and term.