aisha needs a loan to finance her latest startup. she wants a loan with the lowest overall interest costs. she’s considering a 3-year loan with an 8% fixed interest rate or a 5-year loan with a 6% fixed interest rate. why would aisha pick the 3-year loan?
Aisha would pick the 3-year loan with an 8% fixed interest rate because the shorter loan term usually means less total interest paid overall, even if the interest rate is slightly higher.
Why?
- 3 years = less time for interest to build up
- 8% for 3 years can cost less in total than 6% for 5 years
- A lower rate does not always mean lower total interest if the loan lasts much longer
So the main reason is that the shorter repayment period reduces the total interest cost.
Answer: She should choose the 3-year loan because it likely has the lowest overall interest cost.
Başka soruların olursa sormaktan çekinme! 
Why Would Aisha Pick the 3-Year Loan with 8% Interest Over the 5-Year Loan with 6% Interest?
[FORMULA USED:]
Simple interest formula: $$ I = P \times r \times t $$
where P is the principal (loan amount), r is the annual interest rate (as a decimal), and t is the time in years.
(This assumes simple interest, common for comparing total loan costs in basic finance problems when payment details aren’t specified.)
[SOLUTION STEPS:]
Step 1 — Calculate Total Interest for the 3-Year Loan
Interest = P \times 0.08 \times 3 = 0.24P
(8% of principal per year × 3 years = 24% of principal in total interest.)
Step 2 — Calculate Total Interest for the 5-Year Loan
Interest = P \times 0.06 \times 5 = 0.30P
(6% of principal per year × 5 years = 30% of principal in total interest.)
Step 3 — Compare the Total Interest Costs
0.24P < 0.30P
The 3-year loan has a lower total interest cost by 0.06P (or 6% of the principal), regardless of the actual loan amount.
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[ANSWER:] Aisha would pick the 3-year loan because its total interest cost (0.24P) is lower than the 5-year loan’s (0.30P).
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[KEY CONCEPTS:]
1. Simple Interest
- [Definition:] Interest calculated only on the initial principal, not on accumulated interest.
- [In this problem:] Used to directly compare total interest paid over the loan term, as I = P \times r \times t.
2. Total Interest Cost
- [Definition:] The full amount of interest paid over the entire loan period (I).
- [In this problem:] Shorter term with higher rate (3 years at 8%) beats longer term with lower rate (5 years at 6%) because r \times t is smaller (0.24 vs. 0.30).
[COMMON MISTAKES:]
Focusing Only on the Interest Rate
- [Wrong:] “6% is lower than 8%, so pick the 5-year loan.”
- [Right:] Multiply rate by time: effective cost is rate × years.
- [Why it’s wrong:] Ignores how longer terms multiply even low rates into higher totals.
Forgetting the Principal Cancels Out
- [Wrong:] Assuming different principals changes the comparison.
- [Right:] Same P for both, so compare r \times t only.
- [Why it’s wrong:] Problem implies same loan amount for her startup.
Feel free to ask if you have more questions!
Would you like me to calculate this with a specific principal amount (e.g., $10,000) or compare monthly payments?