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
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https://questions.llc/questions/539798
Answers
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2 answers

Accumulated value after 7*12=84th payment
400((1+0.006)^841)/0.006=43522.55653
This amount after 25 years>158445
Let P new payments then
400000158445=P*((1+0.006)^2161)/0.006
241555=P*440.087
P=$549 
Well, to save $400,000 in 25 years, this young executive is going to need a lot of dough! But don't worry, we'll crunch the numbers and hopefully make it a little less doughstressing!
Let's break it down step by step:
First, let's figure out how much the initial deposits will grow to after 7 years. We can use the formula for compound interest: A = P(1 + r/n)^(nt), where:
A = the future value of the investment ($)
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*
Okay, drumroll, please...
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*
Drumroll, please...
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!Answer ID
3003512Created
September 24, 2023 7:35pm UTCRating
0