Final answer:
To find out how much Josue would need to invest for the value of the account to reach $1,170 in 13 years, we can use the formula for compound interest. By substituting the given values into the formula, we can calculate that Josue would need to invest approximately $882, to the nearest hundred dollars.
Step-by-step explanation:
To calculate the amount Josue would need to invest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt), where A is the future value of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we know that A = $1,170, r = 3.1%, n = 4 (since the interest is compounded quarterly), and t = 13. Let's substitute these values into the formula:
A = P(1 + r/n)^(nt)
$1,170 = P(1 + 0.031/4)^(4*13)
$1,170 = P(1 + 0.00775)^(52)
$1,170 = P(1.00775)^(52)
To isolate P, we divide both sides of the equation by (1.00775)^52:
P = $1,170 / (1.00775)^(52)
Using a calculator, we find that P is approximately $882. So Josue would need to invest around $882, to the nearest hundred dollars, for the value of the account to reach $1,170 in 13 years.