Build a savings plan.
Three goals, three formulas, three time horizons. Emergency fund, mid-term goals, retirement — each one a savings problem with the math you've already learned.
Money you need next year and money you need in 40 years cannot live in the same place. The next-year money has to be safe, accessible, predictable — that's a high-yield savings account. The 40-year money has to grow, and it can absorb short-term swings — that's a retirement account.
Every formula in this topic was a tool. This lesson is when you pick which tool fits which drawer. Three goals. Three time horizons. Three vehicles. Same math you've already done — applied to your real life.
Every saving question is a future-value question.
Three columns mapping time horizon to vehicle to typical APY. Short money goes in HYSA, mid money in CDs, long money in retirement accounts. The math is the same family across all three; only the inputs change.
A savings plan is a future-value calculation done in advance: pick a goal amount, a time horizon, an APY you can realistically earn, and solve the right formula for the deposit you need to make today (lump sum) or each month (annuity).
The vehicles your money lives in
- Emergency fund 3 to 6 months of expenses, kept liquid. The first savings goal — before any longer-term investing makes sense.
- HYSA (high-yield savings account) An online savings account paying APYs near the federal funds rate. Where short-term savings live.
- CD (certificate of deposit) A time deposit with a fixed term and rate. Can't withdraw early without penalty. Used for mid-term goals.
- IRA / 401(k) Retirement accounts with tax advantages. Where long-term savings compound for decades. Topic 7 covers what to put inside them.
- Time horizon How long until you need the money. The single biggest factor in choosing a vehicle and a formula.
Time is the biggest lever.
"Person A starts contributing $300/month to a retirement account at age 25 and stops at age 65. Person B does the same thing but starts at age 35. Both earn 7% APR compounded monthly. Both retire at 65. How much does each finish with?"
Set up Person A.
M = $300, r = 0.07, n = 12, t = 40 years. Total contributions: 300 × 12 × 40 = $144,000.
Compute Person A's future value.
Annuity formula. The exponent is 12 × 40 = 480; the periodic rate is 0.07/12 ≈ 0.005833.
Set up Person B.
M = $300, r = 0.07, n = 12, t = 30 years. Total contributions: 300 × 12 × 30 = $108,000. Person B put in only $36,000 less than Person A — three years' worth of contributions.
Compute Person B's future value.
Same formula, different exponent (360 instead of 480).
Compare the gap.
Person A: $787,320. Person B: $365,970. The 10 extra years cost Person B over $421,000 in final balance — even though they only contributed $36,000 less in deposits.
That gap, $421,000 vs. $36,000 of skipped contributions, is the cost of starting late. Time is the biggest lever in long-term saving — bigger than the monthly amount, bigger than the rate.
Three real savings goals. Three appropriate vehicles.
Build an emergency fund: $400/month into a HYSA paying 4.5% APY compounded monthly for 1 year. How much in the fund?
Save for a house down payment: $1,000/month at 5% APR compounded monthly for 5 years.
Save for retirement: $500/month into a 401(k) earning 7% APR compounded monthly for 30 years. What's the balance at the end?
Three fast questions to close out the topic.
Q1. The right vehicle for a 6-month emergency fund is...
Q2. You're 25 and saving for retirement at 65. The right vehicle is...
Q3. Time matters more than monthly contribution amount for long-term saving because...
Saving forward to Topic 7.
Topic 3 ends with a recipe: pick a goal, pick a horizon, run the math. The two DQs and the review apply that recipe to specific scenarios. The Topic 3 cheat sheet has every formula in one place — bookmark it before the ALEKS review.
What's inside your retirement account — stocks, bonds, the index fund vs. the individual name — is Topic 7's job. The math for how much will be there is what you just finished. Compound interest plus time, in every direction.
Two formulas to keep on the tip of your tongue for the rest of the course:
Next: the two Topic 3 DQs apply compound interest and the annuity formula to specific ALEKS-style scenarios. After that, the review pulls all six formulas together one more time before Topic 4 (Loans).
Back to Topic 3Different angle? Need another rep? These are optional — tap any that look helpful.