Question

5) Many persons prepare for retirement by making monthly contributions to a savings program. Suppose that $400 is set aside each month and invested in a savings account that pays 8% interest per year, compounded continuously. a. Determine the accumulated savings in this account at the end of 30 years. b. In Part (a), suppose that an annuity will be withdrawn from savings that have been accumulated at the EOY 30. The annuity will extend from the EOY 31 to the EOY 40. What is the value of this annuity if the interest rate and compounding frequency in Part (a) do not change?

Answer 1

a)

The accumulated savings at the end of 30 years is found using the following equation

Accumulated savings in 30 years = $ 599,388.2

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b)

Using the present value of annuity with continuous compounding, we can find out the value of the annuity

Solving for A in the above equation.

The value of the annuity or annual withdrawls = $ 90,655.37 $ 90,655.4