Marcus can purchase an iPhone on a 2-year loan at 16% simple interest per year. Calculate the future value of a $1,000 loan.

Question

BlackTom AI · Accepted Answer

Simple interest uses A = P(1 + rt).

1) Relevant knowledge points and concepts
- Simple interest: interest = P × r × t, where P is principal, r is annual rate (decimal), t is time in years.
- Future value (amount) for simple interest: A = P + interest = P(1 + rt).
- Distinguish from compound interest where interest is added to principal each period.

2) Step-by-step reasoning
- Given P = $1,000, r = 16% per year = 0.16, t = 2 years.
- Compute the interest earned using simple interest formula: I = P × r × t.

3) Intermediate calculations
- Annual interest: 1000 × 0.16 = 160 (dollars per year).
- Interest for 2 years: 160 × 2 = 320.
- Future value (amount): A = P + I = 1000 + 320 = 1320.

4) Why the correct answer is correct
- The problem explicitly states simple interest at 16% per year for 2 years. Simple interest does not compound; therefore total interest is linear in time: $320. Adding that to the $1,000 principal gives $1,320.00, matching the simple-interest formula result.

5) Why the other options are incorrect
- $2,000.00: This would imply 100% total interest (doubling), which does not follow from 16% for 2 years.
- $1,345.60: This equals 1000 × (1.16)^2 = 1,000 × 1.3456, the future value with annual compounding, not simple interest. The problem specified simple interest, so this is incorrect.
- $1,470.59: This value does not match simple-interest computation for the given rate and time and appears to reflect a different (incorrect) compounding or rate; it is not produced by P(1 + rt) here.

6) Conclusion
The future value using simple interest is $1,320.00, which matches the provided correct answer.

Marcus can purchase an iPhone on a 2-year loan at 16% simple interest per year. Calculate the future value of a $1,000 loan.单项选择题

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