This week's discussion will focus on question two.

The key to understanding the lump sum we would expect to receive today lies in the calculation of the present value of the monthly payments over the 20 years.

The monthly payment is $5,000, and the interest rate is 7.25% per year, compounded monthly.

Formula:

PV = PMT * [(1 - (1 + r)^(-n)) / r],

The present value is represented by PV, the monthly payment is represented by PMT, the monthly interest rate is represented by r, and the number of periods is represented by n.

We calculate the present value with this.

PMT = $5,000

r = 7.25% / 12 = 0.0604 (monthly interest rate)

n = 20 * 12 = 240 (number of periods)

PV = $5,000 * [(1 - (1 + 0.0604)^(-240)) / 0.0604]

PV $691,338.46

The lump sum we would expect to receive today is approximately$691,338.46.

A lump sum payment can make a significant difference by providing instant access to a substantial amount of money. This can be particularly advantageous if we have urgent financial needs or if we're looking to invest the funds elsewhere.

We also have flexibility and control, and we can control how the money is invested, spent, or saved. We can tailor our financial plans according to our specific goals and circumstances.

If we invest the lump sum wisely, we can potentially achieve higher returns than the monthly payments. This opens up opportunities for us to grow our wealth and secure a more prosperous financial future, instilling a sense of optimism.

However, it's crucial to note that managing a large sum of money requires careful planning and financial discipline. Without these, we run the risk of overspending, making poor investment decisions, or even depleting our funds prematurely.

We forfeit the potential future income from the monthly payments by choosing the lump sum. The monthly payments provide security if we have a stable financial situation and prefer a steady income stream.

The erosion of the purchasing power of a lump sum over time can be caused by inflation. If the lump sum is not invested prudently or if the return on investments is surpassed by the inflation rate, the funds may decrease in value.

Which of the following applies to this answer above?

• FP1: The value of any asset is equal to the present value of the cash flows the asset is expected to produce over its economic life.
• FP2: There is a direct relationship between risk and return; as perceived risk increases, required return will also increase (and vice versa), holding other things constant.
• FP3: There is an inverse relationship between price and yield; if an asset's price increases, its return will decrease (and vice versa), holding other things constant.

• PR1: The present value of a cash flow (or an asset) is inversely related to its discount rate; increasing the discount rate decreases the present value (and vice versa), holding other things constant.
• PR2: The timing of the cash flows of an asset is important; sooner is better (later cash flows are more heavily discounted, reducing their present value).
• PR3: The present value of a cash flow (or an asset) is inversely related to its perceived risk; the higher the risk, the higher the discount rate, and therefore the lower the present value.