Question

if you wish to have $800 at the end of five years, and the current market interest rate is 4%,compounded semiannually,how much would you have to deposit today?

Answer 1

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%.