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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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0

URL
https://questions.llc/questions/539798

Answers
2

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1043

2 answers

  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

    Answer ID
    539875

    Created
    May 1, 2011 1:51am UTC

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    0

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  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*

    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
    3003512

    Created
    September 24, 2023 7:35pm UTC

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