Final answer:
Jimmy's investment will take approximately 4 years and 4 months to reach $25,000.
Step-by-step explanation:
To find out how long it will take for Jimmy's investment to reach $25,000, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money Jimmy will have after time t
- P is the initial investment amount ($21,000)
- r is the interest rate (2.66% = 0.0266)
- n is the number of times interest is compounded per year (quarterly = 4)
- t is the time in years
Let's substitute the given values into the formula:
25,000 = 21,000(1 + 0.0266/4)^(4t)
To solve for t, we can use logarithms:
log((1 + 0.0266/4)^(4t)) = log(25,000/21,000)
(4t)log(1 + 0.0266/4) = log(25,000/21,000)
t = log(25,000/21,000) / (4log(1 + 0.0266/4))
Using a calculator, we find that t ≈ 4.03 years.
Since we are asked for the time in years and months, we can convert the decimal part of the years to months:
0.03 years ≈ 4 months
Therefore, it will take Jimmy approximately 4 years and 4 months for his investment to reach $25,000.