Study Tips - Jodonnis Rodriguez

Strong finance problem solving starts with a clear routine. When students see a prompt like a 5-year car loan at 6.5%, a quick timeline, a list of known values, and a short reasonableness check can turn the question into a manageable set of steps. Follow the routine below each time and the formulas become much easier to use with confidence.

01 Draw the timeline

02 List known & unknown

03 Apply the formula

04 Sanity check

A worked example You want to buy a $28,000 car. The dealer offers 5-year financing at 6.5% APR with monthly payments. What's the monthly payment?

Draw the cash flow timeline.

Before reaching for any formula, draw what's happening on a horizontal line of time. Money in goes up, and money out goes down. Mark the unknowns clearly so you know what you're solving for. For a loan, the borrower receives the principal at t = 0 and makes payments out at every subsequent period.

At this point, two things are clear. The unknown is the payment, a single number that repeats. Because the money moves monthly, the interest rate also needs to be monthly. Converting the annual rate before using the formula keeps the timeline and calculation aligned.

List what's known. Mark what's not.

Write the five TVM variables down explicitly with units, then isolate the one you're solving for. This makes the time unit clear before the formula gets involved. It also points you toward the formula with the unknown already isolated.

Known

PV $28,000loan amount, money received

n 60 periods5 years × 12 months

r 0.5417% per month6.5% APR ÷ 12

FV $0loan paid off at end

Unknown

PMT ?

The payment we make each month.

Apply the formula carefully.

Now pick the formula that isolates PMT. Write it down on a fresh line, substitute one value at a time, and do the arithmetic step by step. The intermediate values give you a clean way to check your work.

PMT = PV × r × (1 + r)ⁿ (1 + r)ⁿ − 1

= $28,000 × 0.005417 × (1.005417)⁶⁰ (1.005417)⁶⁰ − 1

= $28,000 × 0.005417 × 1.38282 1.38282 − 1

= 209.74 0.38282

= $547.85 per month

In Excel, the equivalent is =PMT(0.065/12, 60, -28000) which returns the same $547.85. The hand calculation helps confirm the spreadsheet result.

Sanity check before you write it down.

One quick reality check helps confirm the answer before you write it down. Multiply the payment by the number of periods to get total paid, then subtract the loan to get total interest. Ask whether that interest amount feels like the right order of magnitude.

$28,000 principal

$4,871

Principal · 85% Interest · 15%

60 × $547.85 = $32,871.13

The reality checkInterest of about $4,870 on a $28,000 loan over five years is reasonable. A rough back-of-envelope estimate uses an average balance around $14,000 because the loan starts at $28,000 and ends at $0. At 6.5% for 5 years, that gives about $4,550, which is close to the actual figure. ✓

If the units are mismatched by using 5 years for n while keeping the monthly rate, the payment would be about $5,692 per month. The sanity check helps you spot that issue quickly.

Useful checks.

Helpful reminders

Check 01

Match annual rates to monthly periods.

If n = 60 months, then r must be the monthly rate. Divide the APR by 12 before using the formula. Comparing =PMT(0.065, 60, -28000) with =PMT(0.065/12, 60, -28000) shows how much the time unit matters.

Check 02

Use consistent signs.

Excel's TVM functions follow a cash flow convention. Money you receive and money you pay should carry opposite signs. Pick one convention at the start and keep it consistent through the setup.

Check 03

Start with the timeline.

The timeline helps you see the structure of the problem before choosing a formula. Once the timing, cash flows, and unknown are clear, the formula choice is much more straightforward.

Check 04

Finish with a reasonableness check.

A 30-second back-of-envelope check helps confirm the answer before you submit it. If a monthly payment is much larger than the loan amount would suggest, return to the units and the inputs.