A debt of $\$ 4703.79$ is due November 1, 2023. What is the value of the obligation on May 1,2016 , if money is worth 8 \%$ compounded annually?
The value of the obligation is $\$$
(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
\(\boxed{\$2640.66}\) is the value of the obligation on May 1, 2016.
Step 1 :We are given a future value (FV) of $4703.79, an annual interest rate (r) of 8% or 0.08 in decimal form, the interest is compounded annually so n is 1, and the time (t) is the number of years from May 1, 2016 to November 1, 2023 which is approximately 7.5 years.
Step 2 :We can use the formula for present value (PV) which is: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\)
Step 3 :Substituting the given values into the formula, we get: \(PV = \frac{4703.79}{(1 + \frac{0.08}{1})^{1*7.5}}\)
Step 4 :Solving the equation, we find that the present value (PV) is approximately $2640.66
Step 5 :\(\boxed{\$2640.66}\) is the value of the obligation on May 1, 2016.