Final answer:
The lump sum payment of $1 million immediately generally has a greater present value compared to receiving $100,000 per year for the next 10 years. This is because the lump sum can be invested to earn interest over time, which, assuming a positive interest rate, will accumulate to a greater amount than the value of the annuity payments when discounted back to the present value.
Step-by-step explanation:
When deciding whether to take a lump sum payment now or an annuity over a number of years, one must consider the present value of the future payments. The present value refers to the current worth of a stream of future payments, given a specific interest rate. This interest rate is often referred to as the discount rate in financial mathematics.
To determine which option yields a greater present value, we’ll assume an average interest rate or discount rate. However, since the question doesn't specify an interest rate, I will provide a general answer. You won the lottery and have a couple of choices as to how to take the money: receiving a lump sum payment of $1 million immediately is typically considered to have the greater present value because money today can be invested to earn interest over time. On the other hand, receiving $100,000 per year for the next 10 years would yield less in present value terms, due to the future payments being subject to discounting at the presumed interest rate.
If you were to invest the lump sum with an interest rate, you could potentially accumulate a greater amount than the sum of the annuity payments after 10 years. For example, using the formula for compound interest, a lump sum of $1 million could grow significantly. The rate of growth depends on the interest rate you can achieve. For instance, if we use a 7% interest rate, the formula would be $1,000,000(1+0.07)10 which would result in more than $1 million after ten years. Therefore, taking the lump sum could be more beneficial if you plan to invest it at a decent rate of return.