Question

Richard Gorman is 65 years old and about to retire. He had 740000 saved to supplement his pension and social security and would like to withdraw it in equal annual dollar amounts so that nothing is left after 18 years. How much does he have to withdraw each year if he earns 6 percent interest in his money

Answer 1

Richard Gorman should withdraw approximately $64,511.69 each year from his $740,000 savings over 18 years with 6% interest to deplete his retirement funds by the end of this period.

Step-by-step explanation:

To determine how much Richard Gorman must withdraw each year from his $740,000 retirement savings over an 18-year period with a 6 percent annual interest, we must calculate the annuity payment using the formula for the present value of an annuity. The annuity payment formula can be expressed as P = (r*PV) / (1 - (1 + r)^(-n)), where P is the annuity payment, PV is the present value of the annuity, r is the interest rate per period, and n is the number of periods.

Using the formula:

• r (Interest Rate per Period) = 6% annual interest rate, which is 0.06 as a decimal
• n (Number of Periods) = 18 years

We can plug these values into the formula to calculate the annual withdrawal:

P = (0.06 * 740000) / (1 - (1 + 0.06)^(-18))

P = (44400) / (1 - (1.06)^(-18))

P = 44400 / (1 - 0.311804)

P = 44400 / 0.688196

P = $64,511.69 approximately

Therefore, Richard Gorman needs to withdraw approximately $64,511.69 each year to end up with zero balance after 18 years while earning 6 percent interest annually on his remaining balance.

Answer 2

Given that,

Richard Gorman is 65 years old and about to retire.

He had 740000 saved to supplement his pension and social security and would like to withdraw it in equal annual dollar amounts so that nothing is left after 18 years.

Let x be the amount withdraw each year.

Rate of interest is 6%.

Total amount received after 18 years is equal to the amount withdraw each year.

we get,

`18* x=740000*(1+(6)/(100))^(18)`
`x=(740000)/(18)*((106)/(100))^(18)`
`x=(740000)/(18)*(2.854)`
`x=117345.054`

Amount withdraw each year is $117345.054