Final answer:
To have $800 after five years with a 4% semiannual interest rate, you would need to deposit approximately $656.10 today. This is calculated using the present value formula for compound interest.
Step-by-step explanation:
To calculate the amount of money you need to deposit today to have $800 at the end of five years at a 4% interest rate compounded semiannually, you can use the formula for the present value of a future sum with compound interest:
PV = FV / (1 + r/n)ⁿᵗ
Where:
- PV is the present value (amount to deposit today)
- FV is the future value (the amount you want to have in the future)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
Plugging in the values:
FV = $800, r = 4% or 0.04, n = 2 (since it's compounded semiannually), t = 5
The calculation will be:
PV = $800 / (1 + 0.04/2)².⁵
PV = $800 / (1.02)¹⁰
Now calculate:
PV = $800 / (1.21899428)
PV ≈ $656.10
Therefore, you would need to deposit approximately $656.10 today to have $800 in five years with a semiannual compounding interest rate of 4%.