How to Calculate the Lump Sum to Annutiy Conversion

Many insurance, alimony, and divorce settlements, as well as lottery payouts can be received as either an annuity, or a lump sum. An annuity is an agreement where the payee receives a fixed amount every year for a certain number of years. A lump sum is just what the name suggests, a single payment in one big lump.

Most online structured settlement calculators only convert annuity payments into the lump sum value. But you may want to know how much your lump sum is worth in terms of yearly payments at a certain interest rate. The formula below will show you how to do this.

Difficulty: Moderately Easy

Instructions

1. For the moment, call your lump sum payment amount X, and define two new variables as follows:
   n = the number of years in the structured settlement agreement
   r = the annual interest rate.
   
   We will compute a couple of examples to show how the annuity payments differ depending on what values you choose for n and r.

2. Next, learn this formula for converting a lump sum amount into the yearly annuity amount.
   
   Yearly Annuity Payment =
   
   Xr(1+r)^n
   ------------------
   (1+r)^n - 1

3. Now, use the formula to convert a $1,000,000 lump sum into 20 yearly payments at an interest rate of 8%.
   
   [(1000000)(0.08)(1.08)^20]
   --------------------------------------
   [(1.08)^20 - 1]
   
   = 372877/3.66096
   = 101852
   
   So in this example, you would receive $101,852 per year for 20 years.

4. Next, use the same formula to convert a $1,000,000 lump sum into 30 annuity payments at an interest rate of 7%
   
   [(1000000)(0.07)(1.07)^30]
   --------------------------------------
   [(1.07)^30 - 1]
   
   = 532858/6.61226
   = 80586
   
   In this example you receive $80,586 a year for 30 years.