Question

No Excel Please! I am trying to learn the math for the exam! Thank you!!

You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 (in 30 years) and you plan to live to age 99. You want to buy a house costing $300,000 on your 65th birthday and your living expenses will be $30,000 a year after that (starting at the end of year 65 and continuing through the end of year 99, i.e. for 35 years). Assume an annual interest rate of 8%, annual compounding: i) How much will you need to have saved by your retirement date to be able to afford this course of action? ii) Suppose you already have $50,000 in savings today. If you can invest money at 8% a year, how much would you need to save at the end of each year for the next 30 years to be able to afford this retirement plan?

Answer 1

The formula to calculate present value of an annuity is given below:

The present value of annualliving expenses after age 65 is calculated below:

Individual also want to buy a house at age 65 of $300,000.

so, total amount required at age 65 to meet the given course of action is $300,000 + $349,637.0465 = $649,637.0465.

The accumulated amount of current saving 50,000 and annual savings till age 65 must be equal to $649,637.0465.

The formula for accumulation is given below:

The annual amount is calculated below:

Individual must save $1,293.256 at the end of each year.