You wish to retire after 20 years; at which time you want to have accumulated enough money to receive an annuity of $60,000 a year for 25 years of retirement. During the period before retirement you can earn 4 percent annually, while after retirement you can earn 3 percent on your money. What annual contribution to the retirement fund will allow you to receive the 60,000 annually?

$35,085.63

Explanation:

we must first calculate the amount of money that you need to receive $60,000 in annual distributions during 25 years. We must use the present value of an annuity formula:

PV = annuity payment x annuity factor

annuity payment = $60,000

annuity factor (3%, 25 periods) = 17.413

PV = $60,000 x 17.413 = $1,044,780

this means that you will need to save $1,044,780 in the remaining 20 years. The annual contribution can be calculated using the future value of an annuity formula:

FV = annuity payment x annuity factor

Fv = $1,044,780

annuity factor (4%, 20 periods) = 29.778

annuity payment = FV / annuity factor = $1,044,780 / 29.778 = $35,085.63

odd consecutive integers are odd integers that follow each other. they have a difference of 2 between every two numbers. if n is an odd integer, then n, n+2, n+4 and n+6 will be odd consecutive integers. the first number in the pattern is always the variable on its own or in this case, "n". examples.