How to Calculate the Annuity to Lump Sum Conversion

An annuity is a payment plan where a large sum of money is distributed in smaller increments over a period of several year. When a person wins the lottery, or a victim wins a huge settlement from the insurance company, he has a choice between taking the money in one big lump sum, or receiving payments on a yearly basis.

As it turns out, if you add up the all the annuity payments, the amount is more that the lump sum value. If you want to convert an annuity value to its lump sum equivalent, you can calculate it with the formula below.

Difficulty: Easy

Instructions

1. First, you need to identify several variables. The amount of the periodic payment 'M', the total number of payments 'n', and the yearly interest rate 'r'. When you multiply M by n, you get the total amount to be paid; call this number Mn.
   
   For example, if you receive $20,000 a year for 15 years and the yearly nominal interest rate is 7%, then M = 20000, n = 15, r = 0.07, and Mn = 300000.

2. Next, plug those numbers into the annuity-lump sum conversion formula:
   
   Lump Sum =
   
   M[(1+r)^n - 1]
   --------------------
   r(1+r)^n

3. Using the example in Step 1, the present lump sum value of the annuity is
   
   20000[(1.07)^15 - 1]
   -----------------------------
   0.07(1.07)^15
   
   = 20000(1.759)/(0.1931)
   = 182185
   
   If you were to sell this structured settlement now, you would get $182,185. Note that the total value is $300,000.