To find out how much Ray needs to invest today to meet his $130,000 goal, we can use the formula for compound interest, which is:
A = P(1 + (r/n))^(nt)
Where:
A = the future value (amount Ray wants to have at retirement)
P = the principal (the initial amount Ray needs to invest today)
r = the annual interest rate (14%, or 0.14 as a decimal)
n = the number of times interest is compounded per year (semiannually, so n = 2)
t = the number of years (70 - 50 = 20)
Plugging in the values, we get:
130,000 = P(1 + (0.14/2))^(2 * 20)
Now, let's solve for P:
130,000 = P(1 + 0.07)^40
130,000 = P(1.07)^40
Divide both sides by (1.07)^40:
P = 130,000 / (1.07)^40
Using a calculator, we find:
P ≈ $18,587.78
So, Ray needs to invest approximately $18,587.78 today to meet his $130,000 retirement goal.