If you invest $1,000 today at 5% annual interest, compounded once per year, how much will you have in 1 year?

Question

BlackTom AI · Accepted Answer

The compound interest formula for annual compounding is FV = PV × (1 + r)^t, so use PV = $1,000, r = 5% = 0.05, and t = 1 year.

1. Relevant knowledge points and concepts
- Present value (PV) is the initial amount invested.  
- Annual interest rate r must be expressed as a decimal (5% = 0.05).  
- For interest compounded once per year, the future value (FV) after t years is PV × (1 + r)^t. For one year this reduces to a single multiplication by (1 + r).

2. Complete reasoning process step by step
- Convert the percentage rate to a decimal: 5% = 0.05.  
- Since compounding is once per year and the period is one year, apply the formula FV = PV × (1 + r)^1 = PV × (1 + r).  
- Substitute the known values and compute.

3. Calculations with intermediate steps
- 1 + r = 1 + 0.05 = 1.05  
- FV = $1,000 × 1.05  
- FV = $1,000 × 1.05 = $1,050

4. Why the correct answer is correct
- The calculation shows the investment grows by 5% of $1,000, which is $50, so the account balance after one year is $1,000 + $50 = $1,050. Because compounding once per year for one year simply adds one period of 5% growth, $1,050 is the correct future value.

5. Why the other options are incorrect
- $950 would imply a 5% loss (−5%), not a 5% gain.  
- $1,000 implies no interest was earned (0% rate or interest not applied).  
- $1,500 would imply a 50% return in one year, not the 5% given.

6. Conclusion
The correct future value after one year at 5% interest compounded annually is $1,050, which matches the provided answer.

If you invest $1,000 today at 5% annual interest, compounded once per year, how much will you have in 1 year?单项选择题

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