Tyrone, age 25, expects to retire at age 60. He expects to live until age 90. He anticipates needing $45,000 per year in today's dollars during retirement. Tyrone can earn a 12% rate of return and he expects inflation to be 4%. How much must Tyrone save, at the beginning of each year, to meet his retirement goals?
To determine how much Tyrone must save at the beginning of each year to meet his retirement goals, we can use the concept of financial planning called "present value of an annuity."
First, we need to calculate the future value of the retirement expenses. Tyrone expects to need $45,000 per year in today's dollars during retirement. Since inflation is expected to be 4%, we'll need to adjust this amount for inflation.
To adjust for inflation, we can use the formula: Future Value = Present Value x (1 + Inflation Rate)^Number of Years
The number of years in retirement is (90 - 60) = 30 years.
Future Value = $45,000 x (1 + 0.04)^30
Future Value = $45,000 x (1.04)^30
Future Value = $45,000 x 3.24329
Future Value = $145,944.81
So, Tyrone will need a future value of $145,944.81 to cover his retirement expenses.
Next, we need to calculate how much Tyrone must save each year to accumulate this future value by the time he retires. We can use the formula for the present value of an annuity:
Present Value = Annual Payment x [(1 - (1 + Rate)^(-Number of Years))] / Rate
The rate of return for Tyrone is 12%, the number of years is 35 (from age 25 to 60), and the future value is $145,944.81.
Let's substitute these values into the formula:
$145,944.81 = Annual Payment x [(1 - (1.12)^(-35))] / 0.12
To solve for the annual payment, we can rearrange the equation:
Annual Payment = $145,944.81 x (0.12) / [(1 - (1.12)^(-35))]
Now, we can calculate the annual payment:
Annual Payment = $145,944.81 x 0.12 / (1 - 0.27714)
Annual Payment = $145,944.81 x 0.12 / 0.72286
Annual Payment = $17,512.98
Therefore, Tyrone needs to save approximately $17,512.98 at the beginning of each year to meet his retirement goals.