Question

If I deposit $5,000 a year for 10 years, age 25 to 35, at 10% interest, and then let the sum/accumulation sit for 30 years, also earning 10% per year that might be an astute investment. But my older brother who graduated from the “school down south,” says that I should wait until I am 35 and making a ton of money and then I can deposit $7,500 a year for 30 years at 10% and I will be much better off…….since you are a University of Utah grad, and unlike some other universities (Tempe Normal) you can walk and chew gum at the same time, which of the following is correct? Group of answer choices

Both would yield virtually the same sum, within $1,000 of each other without rounding off.

The $5,000 a year would give about $979,258 more because of the power of compound interest.

The $7,500 scenario would provide me with at least $156,786 more.

The $7,500 scenario would provide me with about $156,786 less.

Answer 1

Option 1-Deposit $5,000 a year for 10yr and restit for next 30 years
	Future value of annuity of $5000 deposited evry yearfor 10 years	=	Amount*[{(1=+r)^n -1}/r]
					Amount		=	$5,000
					rate		=	10%
					Time (n)		=	10
	Future value of annuity of $5000 deposited for 10 years	=	$5,000*[{(1+0.1)^10 -1}/0.1]
							=	$5,000*[{1.1)^10 -1}/0.1
							=	$5,000*[{2.5937-1}/0.1]
							=	$5,000*[1.5937/0.1]
							=	$5,000*15.9374
							=	$        79,687.00
	Future value of $79,687 after 30years	=	Amount*(1+r)^n
					Amount		=	$5,000
					rate		=	10%
					Time		=	30years
	Future value of $79,687 after 30years	=	$79,687*(1+0.1)^30
							=	$79,687*(1.1)^30
							=	$79,687*17.4494
		Amount after 40 years from now		=	$ 1,390,490.34
Option 2-Deposit $7,500 a year for 30 years after 10 years fromnow
	Future value of annuity of $5000 deposited every yearfor 10 years	=	Amount*[{(1=+r)^n -1}/r]
					Amount		=	$7,500
					rate		=	10%
					Time (n)		=	30
	Future value of annuity of $5000 deposited for 10 years	=	$57,500*[{(1+0.1)^30 -1}/0.1]
							=	$7,500*[{1.1)^30 -1}/0.1
							=	$7,500*[{17.4494-1}/0.1]
							=	$7,500*[16.4494/0.1]
							=	$7,500*164.4940
	Amount after 40 years from now	=	$ 1,233,705.00
	Difference in both options	=	$1,390,490.34-$1,233,705
							=	$      156,785.34
Answer=	the $7,500 scenario would provide me with about $156,786 less.