To determine the present value \( P \), we need to use the formula for calculating the present value in a situation involving simple interest. The formula is:
[tex]\[ P = \frac{A}{1 + rt} \][/tex]
where:
- \( A \) is the future value you want to achieve.
- \( r \) is the simple interest rate (expressed as a decimal).
- \( t \) is the time the money is invested for, in years.
Given the values:
- \( A = \$5000 \)
- \( r = 1.55\% = 0.0155 \) (as a decimal)
- \( t = 6 \) months, which needs to be converted into years. Since there are 12 months in a year, \( t = \frac{6}{12} = 0.5 \) years.
We substitute these values into the formula:
[tex]\[ P = \frac{5000}{1 + (0.0155 \times 0.5)} \][/tex]
First, calculate the term in the denominator:
[tex]\[ 1 + (0.0155 \times 0.5) = 1 + 0.00775 = 1.00775 \][/tex]
Now divide the future value by this result:
[tex]\[ P = \frac{5000}{1.00775} \approx 4961.55 \][/tex]
Hence, the present value \( P \) that must be invested to achieve the future value of \$5000 after 6 months at a simple interest rate of 1.55% is approximately:
[tex]\[ P \approx \$4961.55 \][/tex]
