Kyoko has 15,000 by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: solve the compound interest formula for the interest rate.)
Answer
Minimum Annual Interest Rate Needed
To find the minimum annual interest rate Kyoko needs to achieve her goal, we will use the compound interest formula:
Future Value (A) = P(1 + r)t
Where:
- A = Future value = $15,000
- P = Present value = $10,000
- r = Annual interest rate (in decimal)
- t = Number of years = 6
Step 1: Plug values into the formula
15000 = 10000 × (1 + r)6
Step 2: Solve for (1 + r)
Divide both sides by 10,000:
1.5 = (1 + r)6
Step 3: Take the 6th root of both sides
Apply the 6th root (or raise both sides to the power of 1/6):
1 + r = (1.5)1/6 ≈ 1.06977
Step 4: Solve for r
r ≈ 1.06977 – 1 = 0.06977
Step 5: Convert to percentage
r ≈ 6.98%
✅ Final Answer:
Kyoko needs a minimum annual interest rate of 6.98% (to the nearest hundredth of a percent) to reach her goal of $15,000 in 6 years.