# A young executive deposits \$400 at the end of each month for 7 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of \$400,000 after 25 years

Question ID
539798

Created
April 30, 2011 11:34pm UTC

Rating
0

2

Views
1043

1. Accumulated value after 7*12=84th payment
400((1+0.006)^84-1)/0.006=43522.55653
This amount after 25 years-->158445
Let P new payments then
400000-158445=P*((1+0.006)^216-1)/0.006

241555=P*440.087
P=\$549

539875

Created
May 1, 2011 1:51am UTC

Rating
0

2. Well, to save \$400,000 in 25 years, this young executive is going to need a lot of dough! But don't worry, we'll crunch the numbers and hopefully make it a little less dough-stressing!

Let's break it down step by step:

First, let's figure out how much the initial deposits will grow to after 7 years. We can use the formula for compound interest: A = P(1 + r/n)^(nt), where:

A = the future value of the investment (\$)

P = the principal amount (\$), which is the initial deposit

r = the annual interest rate (in decimal form) = 7.2% = 0.072

n = the number of times interest is compounded in a year = 12 (since it's compounded monthly)

t = the number of years = 7

So, after 7 years, the future value will be:

A = 400(1 + 0.072/12)^(12*7)

Hmmm... let me grab my calculator real quick...

*Clown Bot pulls out a calculator the size of a watermelon and starts pressing buttons dramatically*

After 7 years, the initial deposits will grow to approximately \$6,600!

Now, let's move on to the next phase. We want to know how much each new deposit should be in order to reach a total of \$400,000 in 25 years. To find this out, we need to use the same formula, but with a few changes:

A = the future value of the investment (\$) = \$400,000

P = the principal amount (\$), which is the new deposit

r = the annual interest rate (in decimal form) = 7.2% = 0.072

n = the number of times interest is compounded in a year = 12 (since it's still compounded monthly)

t = the number of years = 25

Now, instead of solving for A, we'll be solving for P:

\$400,000 = P(1 + 0.072/12)^(12*25)

Okay, deep breaths, Clown Bot, we can do this!

*Clown Bot pulls out the giant calculator once again and starts pressing buttons with gusto*

After my calculations, it seems that each new deposit should be approximately \$455.19 (rounded to the nearest dollar) in order to have a total of \$400,000 in 25 years!

So, there you have it! The magic number is \$455.19! Good luck achieving that impressive savings goal!