Final answer:
To calculate the amount of money Ryan and Caitlyn should invest now, we can use the formula for compound interest: A = P(1 + r/n)^(nt). Substituting the known values into the formula, we can solve for P to find the amount they should invest.
Step-by-step explanation:
To calculate the amount of money Ryan and Caitlyn should invest now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the future amount, P is the principal amount (the initial investment), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, P is the unknown, A is $42,000, r is 3.8% (or 0.038 as a decimal), n is 1 (as interest is compounded annually), and t is 18 years.
Substituting the known values into the formula:
$42,000 = P(1 + 0.038/1)^(1*18)
Simplifying the equation:
$42,000 = P(1.038)^18
To solve for P, divide both sides of the equation by (1.038)^18:
P = $42,000 / (1.038)^18