I thought I understood simple interest – in my head it’s like a parking meter: pay a steady rate for however long you’re parked. But I got confused with a real example. Say I borrow some money at a simple interest rate of 10% per year for 18 months. The note says interest is charged monthly, and I’m planning to make a partial payment (like $200) after 6 months.
Do I just take the yearly rate, scale it by 1.5 years, and calculate the interest on the original amount the whole time? Or should I break it into months and, after that 6‑month payment, switch to calculating the remaining interest on the smaller balance for the rest of the months? Basically: in simple interest, is it always on the original principal no matter what, or does a mid-payment change the principal for the remaining time?
I’m mixing this up with compound interest rules, and I can’t tell which idea belongs where. Any help appreciated!
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3 Responses
Break it into periods: accrue simple interest monthly on the outstanding principal, pay the 6‑month accrued interest first with your $200 and use any remainder to reduce principal, then continue accruing months 7–18 on the reduced principal (no interest on interest) (see https://www.mathsisfun.com/money/simple-interest.html). What principal and exact payment timing do you have so we can compute the totals?
Break it into periods between payments and charge simple interest only on the outstanding principal in each period: compute 6 months’ interest P × 0.10 × (6/12), apply your $200 first to that interest with any leftover reducing principal, then charge 12 more months on the reduced balance (equivalently 0.10/12 per month, no compounding). I once thought simple interest stuck to the original amount too, until a scrappy old car loan taught me that a mid‑payment resets the balance for future interest.
Hey! I love your parking‑meter picture – that’s exactly the right intuition for simple interest. Let’s tidy up the rules and then run a clean example so it all clicks.
Big idea
– Simple interest means interest grows in direct proportion to time and to the amount of principal you still owe. It doesn’t earn interest on interest.
– When you make a payment midstream, the usual order is: it first pays off any interest that has accrued up to that date; whatever is left reduces the principal. From then on, interest is computed on the new (smaller) principal.
– If your payment isn’t even enough to cover the accrued interest, then your principal doesn’t drop yet. Depending on the agreement, that leftover interest usually sits as “unpaid interest” (it typically does not itself accrue interest in a true simple‑interest loan), and interest for future periods is still computed on the original principal until you actually reduce it.
How to compute it (simple, practical steps)
1) Convert the annual simple rate to the time unit you’re using.
– If it says “charged monthly,” use a monthly rate r_m = r/12.
2) Work interval by interval between payments:
– Interest in an interval = (principal at the start of the interval) × (rate) × (length of the interval).
– At a payment date, apply the payment to accrued interest first, and any leftover reduces principal.
3) Repeat until the end.
So, to your question “Do I just scale the yearly rate by 1.5 years on the original amount?”:
– Yes, if there are no payments in the middle (interest = principal × 0.10 × 1.5).
– No, if you make a mid‑payment that’s big enough to reduce principal. In that case, split the timeline and recompute on the reduced principal for the remaining time.
A worked example
Suppose:
– Principal P = $3,000
– Simple annual rate r = 10% = 0.10
– Total time = 18 months
– You make a $200 payment right after month 6.
– Interest is charged monthly (so monthly simple rate = 0.10/12).
Step 1: First 6 months
– Interest over 6 months: I1 = P × r × (6/12) = 3000 × 0.10 × 0.5 = $150.
Step 2: Apply the $200 payment at month 6
– The $200 first pays the $150 interest. That leaves $50 to reduce principal.
– New principal after month 6: P2 = 3000 − 50 = $2,950.
Step 3: Last 12 months (months 7–18)
– Interest over the next 12 months on the new principal:
I2 = P2 × r × (12/12) = 2950 × 0.10 × 1 = $295.
Totals
– Total interest over the 18 months = I1 + I2 = 150 + 295 = $445.
– You’ve already paid $200 at month 6 (150 interest + 50 principal).
– At month 18, you’d still owe the remaining principal ($2,950) plus the last 12 months’ interest ($295), totaling $3,245 at that final payoff. Across the whole loan, you will have paid $3,000 in principal and $445 in interest.
What if your mid‑payment is smaller than the accrued interest?
– Say P = $5,000, r = 10%.
– In 6 months, interest is 5000 × 0.10 × 0.5 = $250.
– If you pay only $100 at month 6, it doesn’t touch principal; $150 of interest remains unpaid. Principal stays $5,000.
– The next 12 months’ interest is then 5000 × 0.10 × 1 = $500, and you still have the unpaid $150 interest from month 6 to settle at some point. There’s no “interest on that interest” in a simple‑interest setup unless your contract says otherwise, but your principal won’t fall until you pay more than the accrued interest.
Rule of thumb to remember
– Simple interest = “parking meter on your current principal.” Pay down principal, and the meter ticks slower from then on. If your payment only covers interest, the meter keeps ticking at the same speed because the principal hasn’t shrunk.
– To compute with any schedule of payments: sum “principal during each interval × rate × time in that interval.”
Nice reference to learn/confirm
– Khan Academy has a friendly walkthrough of simple interest: https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/interest-basics/v/simple-interest
One last practical note
– Lenders may compute interest daily (using a 365- or 360‑day convention) and post it monthly, and they may specify how payments are allocated (fees → interest → principal). The math idea above still holds: compute interest on the outstanding principal for each slice of time, then reduce principal by whatever part of your payment is left after covering accrued interest.
Hope that settles the “which rules go where” feeling. You had the right instinct-break it at the payment, clear the interest, and then keep going on the reduced balance.