If money can earn 5.25% compounded monthly, what is the value of an annuity consisting of annual payments of $2500 continuing for 16 years? The first payment will be received today.
To calculate the value of an annuity, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity (the value of the annuity after 16 years)
P = Annual payment amount ($2500)
r = Interest rate per period (5.25% divided by 12, since compounding is monthly)
n = Number of periods (16 years multiplied by 12 months)
Step 1: Convert the interest rate to a decimal and divide by the number of periods
r = 5.25% / (12 * 100) = 0.0525 / 12 = 0.004375
Step 2: Multiply the number of years by the number of periods per year
n = 16 * 12 = 192
Step 3: Plug the values into the formula and solve for FV
FV = 2500 * [(1 + 0.004375)^192 - 1] / 0.004375
Using a calculator or a spreadsheet, calculate the value of the annuity using the provided formula:
FV = 2500 * [(1 + 0.004375)^192 - 1] / 0.004375
≈ 2500 * [2.8683 - 1] / 0.004375
≈ 2500 * 1.8683 / 0.004375
≈ 4670.75 / 0.004375
≈ $1,067,088.64
Therefore, the value of the annuity after 16 years would be approximately $1,067,088.64.