Final answer:
Paisley needs to invest approximately $935.92, which rounds to $900, to have $1,210 in the account in 6 years with a 3.8% interest rate compounded monthly.
Step-by-step explanation:
To calculate how much Paisley needs to invest to have $1,210 in 6 years at an interest rate of 3.8% compounded monthly, the formula for compound interest is used:
P = A / (1 + r/n)^(nt)
Where:
P is the principal amount (the initial amount of money)A is the future value of the investment/loan, including interestr is the annual interest rate (decimal)n is the number of times that interest is compounded per yeart is the number of years the money is invested/borrowed for
Given A=$1,210, r=0.038 (3.8%), n=12, and t=6, we substitute these values into the formula:
P = 1210 / (1 + 0.038/12)^(12*6)
Solving the equation gives us:
P ≈ $935.92
Rounded to the nearest hundred dollars, Paisley needs to invest $900.