To determine how many years it will take for Emmanuel’s investment to grow to $1,500 with simple interest, we use the simple interest formula:

$A = P(1 + rt)$

where:

• $A$ is the future value (final amount)
• $P$ is the principal (initial investment)
• $r$ is the annual interest rate (in decimal form)
• $t$ is the time in years

Step 1: Substitute known values

• $A = 1500$
• $P = 1000$
• $r = 2.5\% = 0.025$

$1500 = 1000(1 + 0.025t)$

Step 2: Solve for $t$

1. Divide both sides by 1000:

   $1.5 = 1 + 0.025t$

2. Subtract 1 from both sides:

   $0.5 = 0.025t$

3. Divide both sides by 0.025:

   $t = \frac{0.5}{0.025} = 20 \, \text{years}$

Final Answer

It will take 20 years for Emmanuel’s account to reach a balance of $1,500.

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Would you like a more detailed explanation or have further questions?

Here are 5 related questions:

1. What is the difference between simple and compound interest?
2. How much would Emmanuel’s balance be after 10 years?
3. If the interest rate increased to 5%, how long would it take to reach $1,500?
4. How can you calculate the total interest earned in a simple interest problem?
5. What happens if Emmanuel deposits more money into the account over time?

Tip: In simple interest, the interest earned each year is constant since it is only applied to the principal.