Saving 9

An amount of $ 2000 is invested at an interest of 5% per month. If $ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount has accumulated first exceed $ 42000.

Correct answer:

n =  42

Step-by-step explanation:

x0=2000 x1=x0 1.05+200=2000 1.05+200=2300 x2=x1 1.05+200=2300 1.05+200=2615 x3=x2 1.05+200=2615 1.05+200=117834=294534=2945.75 x4=x3 1.05+200=2945.75 1.05+200=3293.0375 x5=x4 1.05+200=3293.0375 1.05+2003657.6894 x6=x5 1.05+200=3657.6894 1.05+2004040.5738 x7=x6 1.05+200=4040.5738 1.05+2004442.6025 x8=x7 1.05+200=4442.6025 1.05+2004864.7327 x9=x8 1.05+200=4864.7327 1.05+2005307.9693 x10=x9 1.05+200=5307.9693 1.05+2005773.3678 x11=x10 1.05+200=5773.3678 1.05+2006262.0361 x12=x11 1.05+200=6262.0361 1.05+2006775.138 x13=x12 1.05+200=6775.138 1.05+2007313.8949 x14=x13 1.05+200=7313.8949 1.05+2007879.5896 x15=x14 1.05+200=7879.5896 1.05+2008473.5691 x16=x15 1.05+200=8473.5691 1.05+2009097.2475 x17=x16 1.05+200=9097.2475 1.05+2009752.1099 x18=x17 1.05+200=9752.1099 1.05+20010439.7154 x19=x18 1.05+200=10439.7154 1.05+20011161.7012 x20=x19 1.05+200=11161.7012 1.05+20011919.7862 x21=x20 1.05+200=11919.7862 1.05+20012715.7755 x22=x21 1.05+200=12715.7755 1.05+20013551.5643 x23=x22 1.05+200=13551.5643 1.05+20014429.1425 x24=x23 1.05+200=14429.1425 1.05+20015350.5997 x25=x24 1.05+200=15350.5997 1.05+20016318.1296 x26=x25 1.05+200=16318.1296 1.05+20017334.0361 x27=x26 1.05+200=17334.0361 1.05+20018400.7379 x28=x27 1.05+200=18400.7379 1.05+20019520.7748 x29=x28 1.05+200=19520.7748 1.05+20020696.8136 x30=x29 1.05+200=20696.8136 1.05+20021931.6543 x31=x30 1.05+200=21931.6543 1.05+20023228.237 x32=x31 1.05+200=23228.237 1.05+20024589.6488 x33=x32 1.05+200=24589.6488 1.05+20026019.1313 x34=x33 1.05+200=26019.1313 1.05+20027520.0878 x35=x34 1.05+200=27520.0878 1.05+20029096.0922 x36=x35 1.05+200=29096.0922 1.05+20030750.8968 x37=x36 1.05+200=30750.8968 1.05+20032488.4417 x38=x37 1.05+200=32488.4417 1.05+20034312.8637 x39=x38 1.05+200=34312.8637 1.05+20036228.5069 x40=x39 1.05+200=36228.5069 1.05+20038239.9323 x41=x40 1.05+200=38239.9323 1.05+20040351.9289 x42=x41 1.05+200=40351.9289 1.05+20042569.5253 n=42=42

Did you find an error or inaccuracy? Feel free to write us. Thank you!


You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • Investment
    penize 1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
  • Loan
    loan Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
  • Investment 2
    exp_growth2 Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi
  • Slow saving in banks
    penize How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?
  • Interest
    dollars Calculate how much you earn for $n years $x deposit if the interest rate is $p% and the interest period is a quarter.
  • Future value
    penize Suppose you invested $1000 per quarter over a 15 years period. If money earns an anual rate of 6.5% compounded quarterly, how much would be available at the end of the time period? How much is the interest earn?
  • Savings
    500eur The depositor regularly wants to invest the same amount of money in the financial institution at the beginning of the year and wants to save 10,000 euros at the end of the tenth year. What amount should he deposit if the annual interest rate for the annua
  • Deposit
    ping_bank If you deposit 719 euros at the beginning of each year, how much money we have at 1.3% (compound) interest after 9 years?
  • Retirement annuity
    bankovka How much will it cost to purchase a two-level retirement annuity that will pay $2000 at the end of every month for the first 10 years, and $3000 per month for the next 15 years? Assume that the payment represent a rate of return to the person receiving th
  • When will I be a millionaire?
    milionar_kedy $name monthly send $money euros to the bank, which he deposits bear interest of $p% p. A. Calculate how many months must $name save to save $total euros? Inflation, interest rate changes, or bank failures ignore.
  • Two accounts
    bank A banker divided $5000 between 2 accounts, one paying 10% annual interest and the second paying 8% annual interest. Express the amount invested in the 10% account in the terms of the amount invested in the 8% account.
  • Compound interest 3
    exp_growth2 After 8 years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly? (interest is now dream - in the year 2019)
  • Semiannually compound interest
    bank2 If you deposit $5000 into an account paying 8.25% annual interest compounded semiannually, how long until there is $9350 in the account?
  • Suppose 3
    penize Suppose that a couple invested Php 50 000 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually, a, Give an exponential model for the situation b, Will the money be
  • Simple interest 2
    coins-uk Find the simple interest if $x USD at $p% for $m months.
  • A loan
    exp_growth A loan in the amount of $944 is charged simple interest at an annual rate of 8.1%. How much money is owed 14 months after the loan was made?
  • Interest
    MoneyHouse What is the annual interest rate on your account if we put $x and after $n days received $y?