VIPSolutions( Solving for i ) Puck Van Houten , who has been married for 2 1 years , would like to buy their partner an expensive diamond ring with a platinum setting on their 3 0 - year wedding anniversary. Assume that the cost of the ring will be $ 1 3 , 0 0 0 in 9 years. Puck currently has $ 4 , 5 3 4 to invest. What annual rate of return must Puck earn on their investment to accumulate enough money to pay for the ring? Question content area bottom Part 1 The annual rate of return Puck must earn on their investment to accumulate enough money to pay for the ring is ( type your answer as a percentage, round to two decimal places ) enter your response here % .
Question:
( Solving for i ) Puck Van Houten , who has been married for 2 1 years , would like to buy their partner an expensive diamond ring with a platinum setting on their 3 0 - year wedding anniversary. Assume that the cost of the ring will be $ 1 3 , 0 0 0 in 9 years. Puck currently has $ 4 , 5 3 4 to invest. What annual rate of return must Puck earn on their investment to accumulate enough money to pay for the ring? Question content area bottom Part 1 The annual rate of return Puck must earn on their investment to accumulate enough money to pay for the ring is ( type your answer as a percentage, round to two decimal places ) enter your response here % .
This is AI generated Response.
Asked by: Veera manikanta
Created at: 2025-07-28 06:23:00
Asked by: Veera manikanta
Created at: 2025-07-28 06:23:00
Final Answer:
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Let's break down the problem:
- **Future Value (FV):** \$13,000 (cost of the ring in 9 years)
- **Present Value (PV):** \$4,534 (amount Puck currently has)
- **Number of years (n):** 9
- **Annual interest rate (i):** ?
The formula for future value with annual compounding is:
\[
FV = PV \times (1 + i)^n
\]
Plug in the numbers:
\[
13,000 = 4,534 \times (1 + i)^9
\]
Divide both sides by 4,534:
\[
\frac{13,000}{4,534} = (1 + i)^9
\]
\[
2.867 = (1 + i)^9
\]
Now, take the 9th root of both sides:
\[
1 + i = (2.867)^{1/9}
\]
\[
1 + i = 1.1226
\]
\[
i = 1.1226 - 1 = 0.1226
\]
\[
i = 12.26\%
\]
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**Final Answer:**
The annual rate of return Puck must earn on their investment to accumulate enough money to pay for the ring is:
\[
\boxed{12.26\%}
\]
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