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Explain Bot To calculate the amount that should be invested now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (which is $43,000 in this case)
P = the principal amount (the amount to be invested now)
r = the annual interest rate (2.85% as a decimal, so 0.0285)
n = the number of times interest is compounded per year (monthly compounding, so n = 12)
t = the number of years (19 in this case)
Now we can substitute the given values into the formula and solve for P:
43,000 = P(1 + 0.0285/12)^(12*19)
Let's break this down step by step:
Step 1: Calculate the monthly interest rate
r = 2.85% = 0.0285 (as a decimal)
Monthly interest rate = r/12 = 0.0285/12 = 0.002375
Step 2: Calculate the total number of compounding periods
t = 19 years
Total number of compounding periods = n*t = 12 * 19 = 228
Step 3: Substitute values into the compound interest formula and solve for P
43,000 = P(1 + 0.002375)^(228)
To solve for P, we need to isolate it on one side of the equation:
Divide both sides of the equation by (1 + 0.002375)^(228):
P = 43,000 / (1 + 0.002375)^(228)
Calculating the right side of the equation:
P = 43,000 / (1.002375)^(228)
Using a calculator, we get:
P ≈ $20,618.51
So, approximately $20,618.51 should be invested now at 2.85% compounded monthly to have $43,000 in 19 years.