Question

# Naomi is a​ 20-year old college student with an assignment to write out her plans for...

Naomi is a​ 20-year old college student with an assignment to write out her plans for retirement. She is investigating several ways she can accumulate​ \$1 million by the time she is 50 years old. She is considering a​ long-term certificate of deposit​ (CD) that pays

2

​%

annually and an annuity that returns

3

​%

annually. She also did research and found that the average​ long-term return from stock market investments is between

9

​%

and

11

​%.

Answer parts 1 through 5 to help her calculate how much money she will need to deposit each year to accumulate​ \$1 million.

Click the icon to view the​ \$1.00 Sinking Funds Payments table.

Click the icon to view the Future Value of​ \$1.00 Ordinary Annuity table.

Click the icon to view the Compound Interest of​ \$1.00 table.

1. Calculate the amount Naomi will need to deposit each year into the CD at

2

​%

for 30 years to accumulate​ \$1 million.

The deposit for the CD each year will be

​\$nothing

.

​(Round to nearest cent as​ needed.)

Solution:

Required future value = \$1 million

Period = 30 years

Interest rate = 2%

It is not given in question that Naomi will deposit the amount at beginning of each year or ending of each year, therefore we will calculate the amount deposited every year in each scenario.

If deposit made at beginning of each year starting on her 20th birthday:

Let annual deposit is X

Now

X * Cumulative FV factor for annuity due at 2% for 30 periods = \$1,000,000

X * 41.37944 = \$1,000,000

X = \$24,166.59

If deposit made at end of each year:

Let annual deposit is X

Now

X * Cumulative FV factor for ordinary annuity at 2% for 30 periods = \$1,000,000

X * 40.56808 = \$1,000,000

X = \$24,649.92