Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity

The lump sum be of $237,228.84

Explanation:

In order to calculate how large must the lump sum be we would have to use and calculate the formula of Present value of annuity due as follows:

Present value of annuity due = (1+interest rate) * Annuity[1 - (1+interest rate) ^-time period]/rate

Present value of annuity due = (1+0.075) * $25,000[1 - (1.075) ^-15]/0.075

Present value of annuity due=$25,000*9.489153726

Present value of annuity due=$237,228.84 (Approx)

The lump sum be of $237,228.84