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



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




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

Related math problems and questions:

  • Investment 2
    exp_growth2 Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi
  • Investment
    penize 1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
  • 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?
  • 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?
  • 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.
  • Deposit
    ping_bank If you deposit $x euros at the beginning of each year, how much money we have at $p% (compound) interest after $n 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
  • You take
    exp_growth You take out Php 20 000 loan at 5% interest rate. If the interest is compounded annually, a. Give an exponential model for the situation b. How much Will you owe after 10 years?
  • 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
  • If you 3
    bank2 If you deposit $4500 at 5% annual interest compound quarterly, how much money will be in the account after 10 years?
  • How much 2
    bank2 How much money would you need to deposit today at 5% annual interest compounded monthly to have $2000 in the account after 9 years?
  • If you 2
    exp_growth If you deposit $4000 into an account paying 9% annual interest compounded monthly, how long until there is $10000 in the account?
  • Compound interest
    bank Compound interest: Clara deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Both money and interest remain deposited in the bank. How many CZK will be in the bank after 3 years?
  • Common ratio
    growth If 200 units of a commodity are consumed in a first year, and if the annual rate of increase in consumption is 5% (a) what amount is consumed in the 8th year; (b) in the first 15 years?
  • 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?
  • Bank
    money Paul put $a in the bank for $r years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is $u%, and the tax on interest is $d%.
  • 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