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Apply the formula A=Pert, where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time in years. Dora invests $5,000 in an account that is compounded continuously at an annual interest rate of 2.5%. In 10 years, how much will Dora's investment be worth to the nearest dollar? Show steps that Dora must take to solve this problem.
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GPT-5 mini
AI
Use the continuous compounding formula A = P e^{rt}.
1. Identify values: P = 5000, r = 0.025 (2.5% as a decimal), t = 10.
2. Compute exponent: rt = 0.025 × 10 = 0.25.
3. Compute A: A = 5000 · e^{0.25} ≈ 5000 · 1.2840254167 ≈ 6420.1270834.
4. Round to the nearest dollar: A ≈ $6,420.
Dora's investment will be worth about $6,420 in 10 years.
1. Identify values: P = 5000, r = 0.025 (2.5% as a decimal), t = 10.
2. Compute exponent: rt = 0.025 × 10 = 0.25.
3. Compute A: A = 5000 · e^{0.25} ≈ 5000 · 1.2840254167 ≈ 6420.1270834.
4. Round to the nearest dollar: A ≈ $6,420.
Dora's investment will be worth about $6,420 in 10 years.
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