Future value with periodic

rates.

Denise has her heart set on being a millionaire. She decides that at the end of every year, she will put away

$4,000

into her "I want to be a millionaire account" at her local bank. She expects to earn

6%

annually on her account.

a. How many years must Denise faithfully put away her money to succeed at becoming a millionaire?

b.If Denise switches to a monthly savings plan and puts one-twelfth of the

$4,000

away each month

($333.33),

how much will she have in

48

years at the

6%

APR?

c.Why is the future value under the monthly savings plan more than the

$1,000,000

goal?

Next, let's assume Denise is now thirty-five years old and thus has thirty years for saving toward her one-million-dollar goal. She anticipates an APR of

9%

on her investments.

d. How much does she need to save each year to become a millionaire by age sixty-five if she puts money away annually?

e.How much does she need to save if she puts money away monthly?

f.Why does it take more per month when she is putting money away at

9%

than when she was earning a lower rate of

6%

over the

48

years?

Note:Ignore the effect of taxes on your calculations.