TOPIC 3 · DQ 1 / Savings / discussion question

01Plug the formulas in. Watch them work.

Four problems on the Financial tab walk you through every future-value formula in this topic — simple, compound, annuity, and the reverse "how much do I save each month?" calculation.

Discussion · 5 pts Initial post Wed · replies Sun Future value Annuity FV

▸ The why · 7-slide reference

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Step 1 · materials

Download the worksheet

Topic_3_DQ_1.xlsx

XLSX 5 pts v · spring 26

Step 2 · walkthrough

Watch the click-by-click

Every keystroke for all four problems. The Scribe walkthrough lands here once recorded; for now, the Excel template above is your working surface.

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Step-by-step walkthrough

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Same walkthrough, two modes. Use whichever helps you today.

Open the Financial tab. Type your name in the blue cell at the top — the inputs (P, r, t) for the four problems are generated from your name, so your version is unique. The four problems map directly to the topic's four future-value formulas. Self-check colors tell you whether each answer cell got the right value and whether you used a formula to get there. Both have to be green for credit. New to the cell color codes? See the legend.

§1 · Simple interest

FV = P(1 + rt).

One-time deposit, no compounding. Lesson 2's formula, in spreadsheet form.

§2 · Compound interest

FV = P(1 + r/n)^(nt).

Same deposit, now compounded n times per year. Lesson 3's formula.

§3 · Annuity (forward)

FV = P((1+r/n)^(nt) − 1)/(r/n).

Stream of monthly deposits of P each. Lesson 5's annuity FV formula.

§4 · Solve for M

P = FV(r/n)/((1+r/n)^(nt) − 1).

Reverse direction: how much do I save each month to reach a target FV? The most useful formula in personal finance.

Problem 1 · Simple

Simple interest, cell-reference style.

Problem 1: Simple interest, one-time deposit. You're given P, r, n=12 (always monthly compounding for these problems), and t. You compute the future value FV using the simple-interest formula, then the interest earned (FV − P).

The Excel formula goes into the gold cell: =B20*(1+C20*E20) — where B20 is your randomized P, C20 is your randomized r (already as a decimal), and E20 is t. Note that n doesn't appear; simple interest doesn't compound.

Interest earned: subtract P from FV. =H17-B20 in the gold cell next to it. The sheet checks that you used a subtraction formula, not the typed difference.

This is the same recipe from Lesson 2, just with cell references replacing the numbers.

Problem 2 · Compound

Compound interest, parens matter.

Problem 2: Compound interest, one-time deposit. Same P, r, n, t — but now the formula is FV = P(1 + r/n)^nt. The compounding frequency n now matters: with n=12, interest compounds monthly during the time period.

The Excel formula: =B24*(1+C24/D24)^(D24*E24). Watch every parenthesis. The exponent D24*E24 needs to be in parentheses because Excel evaluates ^ right-to-left and treats ^a*b very differently from ^(a*b).

Interest earned: same idea — =H21-B24.

Sanity check against simple: with the same inputs, compound should give a slightly larger FV. If your simple answer is bigger than your compound answer, a parenthesis is in the wrong place.

Problem 3 · Annuity

A stream of deposits, compounded.

Problem 3: Annuity FV (periodic deposits). Now P is a monthly deposit (not a starting principal). You're given the monthly amount, r, n=12, and t. The formula is the annuity future value from Lesson 5: FV = P · ((1 + r/n)^nt − 1) / (r/n).

The Excel formula: =B29*((1+C29/D29)^(D29*E29)-1)/(C29/D29). The big trap on this row is the dual use of (1+r/n)^(nt) − 1 inside one bracket — you have to subtract 1 before dividing by r/n. The structure: numerator is everything in the outer brackets minus 1; denominator is r/n.

This problem also asks for total invested (=B29*D29*E29 = P times n times t = monthly amount × 12 × years) and interest earned (FV − total invested). The interest-earned figure is usually surprisingly large — that's compounding doing the work over time.

Problem 4 · Reverse

The same formula rearranged for M.

Problem 4: Solve for M to reach a goal. The reverse direction. You're given a future-value goal (generated from your previous answer to Problem 2 or Problem 3), r, n, t. You compute the monthly payment that gets you there. The formula is the annuity formula solved for P:

P = FV · (r/n) / ((1 + r/n)^nt − 1)

The Excel formula: =B34*(C34/D34)/((1+C34/D34)^(D34*E34)-1). Notice the denominator is the same (1+r/n)^(nt) − 1 structure from Problem 3 — you're just rearranging the equation.

Then total invested (=H31*D34*E34) and interest earned (=B34-I31). Note interest in this case is FV − total invested, since the goal is the FV.

This is the most practical formula in the whole topic — it answers "how much do I need to save each month to hit $X by year Y?", which is the Topic 6 finale question made concrete.

Rule

Why =FV() and =PMT() are off-limits.

The DQ instructions are explicit: do not use the built-in =FV() and =PMT() functions. You have to type the formulas manually with cell references and arithmetic operators.

Two reasons. First: writing the formula yourself is the actual skill the DQ is testing. Excel's =FV() takes a different parameter order from the textbook formula, and it returns negative numbers for some sign conventions — using it without understanding it is a recipe for wrong-sign answers. Second: Major Assignment 2 in Topic 4 reuses the same formula shapes with a different scenario (loans). If you've typed FV = P(1+r/n)^(nt) by hand once, the loan amortization formula in MA2 is the same finger memory.

The self-check on the Financial tab catches this: if you plug in the right number directly without using a formula, the cell turns gold (right answer, no formula) instead of green (right answer, formula used). Gold means you got the answer but skipped the skill.

=FV(...)

built-in

rejected by this DQ
different param order
different sign convention

=B24*(1+C24/D24)^(D24*E24)

manual formula

required by this DQ
matches textbook
same shape used in MA2

Common slips

Five mistakes this DQ punishes.

Read these before you submit. The parenthesis slips on Problem 2 and Problem 3 are by far the most common.

01

Used =FV() or =PMT().

Explicitly off-limits for this DQ. The instructor catches it via the self-check; the cell turns gold (right number, no formula) instead of green. Type the formula manually with cell references and arithmetic operators.
02

Wrong parentheses on the exponent.

(1+r/n)^n*t means (1+r/n)ⁿ × t — totally different from (1+r/n)^n×t. Wrap the exponent: (1+r/n)^(n*t). Always.
03

Used the rate as 5 instead of 0.05.

The randomized r in the green cells is already a decimal (e.g. 0.05 for 5%). Don't multiply by 100 again. If your FV is wildly bigger than your principal, this is usually why.
04

Confused P (principal) with P (monthly payment).

Problem 1 and 2 use P as a one-time principal deposit. Problems 3 and 4 use P as a monthly periodic payment (or M). The formulas look similar; the meaning of P doesn't.
05

Subtracted 1 in the wrong place.

The annuity formula's structure is P × ((1+r/n)^(nt) − 1) / (r/n). The − 1 goes inside the outer brackets, not at the end. Misplace it and your answer is roughly wrong by a factor of (1+r/n)^(nt).

Application & connection

From this DQ into MA2.

This DQ exercises four formulas you already know: Lesson 2 (simple interest, FV = P(1+rt)), Lesson 3 (compound interest with frequency, FV = P(1+r/n)^nt), and Lesson 5 (annuity future value, both forward and reverse). The Excel template is your place to confirm: same recipe, different inputs, formula auto-updates if a value changes.

What I'm watching in your formulas: the parentheses around (1 + r/n), the exponent shape ^(n*t) not ^n*t, and that you wrote the formula yourself instead of leaning on Excel's built-in =FV() or =PMT(). Those are explicitly off-limits for this DQ — partly because building the formula by hand is the actual skill, and partly because Major Assignment 2 in Topic 4 (loans) uses the same formula shapes with new labels. Get fluent here, save time there.