Answer: $ 3426
Explanation:
To calculate the amount Josh got back after investing $2500 at a rate of 5% for 6 years and 4 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount,
P is the principal amount (or initial investment),
r is the annual interest rate (which is written as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
For this problem, the principal amount is $2500, the annual interest rate is 5% (or 0.05 as a decimal), the number of times interest is compounded per year is 1, and the time is 6 years and 4 months.
Since the compound interest equation is calculated through the number of years, we need to convert the time in the problem to years. Since there are 12 months in a year, 4 months is equal to 4/12 = 1/3 years. Therefore, the total time is 6 + 1/3 years.
Now, we can plug in the values into the formula:
A = 2500(1 + 0.05/1)^(1*(6 + 1/3))
Calculating this expression, we get:
A = 2500(1 + 0.05)^(19/3)
A = 2500(1.05)^(19/3)
A ≈ 2500(1.05)^6.33
Using a calculator, we see that (1.05)^6.33 is approximately 1.3704.
Multiplying this value by $2500, we get:
A ≈ 2500 * 1.3704
A ≈ $3426
Therefore, the amount Josh got back after investing $2500 at a rate of 5% for 6 years and 4 months is approximately or about $3426.