i need to earn 61000 over 5 years. at 6% interest semiannually what is my first deposit?

To calculate the first deposit needed to earn $61,000 over 5 years at a 6% interest rate compounded semiannually, we can use the present value formula for compound interest:

P = A / (1 + r/n)^(n*t)

Where:
P = Principal amount (first deposit)
A = Future amount (goal of $61,000)
r = Annual interest rate (in decimal form, so 6% becomes 0.06)
n = Number of compounding periods per year (semiannually, so 2)
t = Number of years (5)

Substituting the known values into the formula:

P = 61000 / (1 + 0.06/2)^(2*5)

First, calculate the part inside the parentheses:

1 + 0.06/2 = 1.03

Then raise it to the power of (2*5):

(1.03)^(10) ≈ 1.343916

Finally, divide the future amount by this result:

61000 / 1.343916 ≈ $45,402.35

Therefore, the approximate first deposit needed to earn $61,000 over 5 years at a 6% interest rate compounded semiannually is $45,402.35.