Question

You estimate that by the time you retire in 35 years, you will have accumulated savings of 2 million. The interest rate is 8% and you live 15 years after retirement. a. What annual level of expenditure will those savings support? b. Inflation will eat into the value of your retirement income. Assume a 4% inflation rate and work out a spending program for your retirement that will allow you to increase your expenditure in line with inflation.

Answer 1

The annual expenditure from a $2 million retirement savings with an 8% interest rate over 15 years, we use the annuity formula. Inflation at a 4% rate must be considered by adjusting the annual withdrawals to maintain purchasing power throughout the retirement period.

Step-by-step explanation:

The annual level of expenditure that a savings of 2 million at an interest rate of 8% will support over 15 years of retirement, we need to calculate the equal annual withdrawals that can be taken from this savings, also known as the annuity. This can be calculated using the annuity formula:

P = (PV * r) / [1 - (1 + r)⁻ⁿ]

Where P is the annual payment, PV is the present value of the annuity, r is the annual interest rate, and n is the number of periods.

In this case, PV equals 2 million, r equals 0.08 (8%), and n equals 15. Substituting these values into the formula gives us the annual expenditure.

Regarding inflation adjustments, the inflation rate of 4% needs to be factored in to ensure that purchasing power is maintained. This requires adjusting the annuity payments for inflation by increasing the payments each year by the rate of inflation, creating a growing annuity.