You put $1,000 into a savings account today that offers a 5% APR with semi-annual compounding (i.e., two times per year).

So what is a question in your sum

To calculate the future value of your savings account, you can use the formula for compound interest:

Future Value (FV) = P(1 + r/n)^(nt)

Where:
P = Principal amount (initial investment) = $1,000
r = Annual interest rate (in decimal form) = 5% or 0.05
n = Number of times interest is compounded per year = 2 (semi-annual compounding)
t = Number of years = unknown

Now, let's solve for the future value:

FV = $1,000(1 + 0.05/2)^(2t)

To find the future value after a specific number of years, you need to know the value of 't'. If you have a specific value of 't' in mind, please provide it so that we can proceed with the calculation.

To calculate the future value of your savings account with semi-annual compounding, we can use the formula for compound interest:

Future Value = Principal * (1 + Interest Rate / Frequency)^(Number of Periods * Frequency)

In this case, the principal is $1,000, the interest rate is 5%, and the compounding frequency is semi-annual (twice per year). The number of periods is not specified, so let's assume you are planning to keep the money in the account for 5 years.

Now, let's calculate the future value:

Interest Rate = 5% = 0.05
Compounding Frequency = Semi-annual = 2
Number of Periods = 5 years = 5

Future Value = $1,000 * (1 + 0.05 / 2)^(5 * 2)

First, divide the interest rate by the compounding frequency: 0.05 / 2 = 0.025

Next, multiply the number of periods by the compounding frequency: 5 * 2 = 10

Calculate the raised value: (1 + 0.025)^10 = 1.280084576

Finally, multiply the principal by the raised value: $1,000 * 1.280084576 = $1,280.08

Therefore, the future value of your savings account after 5 years with semi-annual compounding would be approximately $1,280.08.