Question

Pensions Eleni, who is now 50 years old, is employed by a firm that guarantees her a pension of $40,000/year at age 65. What is the present value of her first year’s pension if inflation over the next 15 years is (a) 3%? (b) 4%? (c) 6%? Assume that inflation is continuously compounded.

Answer 1

The present value of Eleni's pension depends on the inflation rate. At 3% inflation, the present value is approximately $25,464.54; at 4% inflation, it is approximately $21,967.11; and at 6% inflation, it is approximately $16,258.85. This shows the decrease in present value with increasing inflation.

Step-by-step explanation:

The student's question involves calculating the present value of a pension at age 65 in today's dollars, considering different rates of inflation over the next 15 years. The present value tells us how much a future sum of money is worth today given a specific rate of inflation, which diminishes the purchasing power of money over time.

To calculate the present value (PV), we use the formula:

PV = P / e^(rt)

• Where P is the future value of the pension, which is $40,000
• e is the base of the natural logarithm
• r is the annual inflation rate (expressed as a decimal)
• t is the number of years until payment (15 years in this case)

Let's calculate the present value for each of the given inflation rates:

1. For an inflation rate of 3% (0.03):
2. PV = $40,000 / e^(0.03*15)
3. PV = $40,000 / e^(0.45)
4. PV = $40,000 / 1.5707
5. PV ≈ $25,464.54

1. For an inflation rate of 4% (0.04):
2. PV = $40,000 / e^(0.04*15)
3. PV = $40,000 / e^(0.60)
4. PV = $40,000 / 1.8221
5. PV ≈ $21,967.11

1. For an inflation rate of 6% (0.06):
2. PV = $40,000 / e^(0.06*15)
3. PV = $40,000 / e^(0.90)
4. PV = $40,000 / 2.4596
5. PV ≈ $16,258.85

These calculations demonstrate how the present value of Eleni's pension decreases as the inflation rate increases.