Savings

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 annual interest period is 2% and the interest tax is 19%? Assume that the depositor will not withdraw deposits or interest during the entire savings period and the annual interest rate will always be the same.

Correct answer:

a =  914.43 Eur

Step-by-step explanation:

$$\begin{gathered} r_1=2\mathrm{\%}={\displaystyle \frac{2}{100}}=0.02 \\ {r}_2=19\mathrm{\%}=1-{\displaystyle \frac{19}{100}}=0.81 \\ q=1+r_1\cdot r_2=1+0.02\cdot 0.81=1.0162 \\ 10000=a\cdot q^{10}+a\cdot q^9+a\cdot q^8+a\cdot q^7+a\cdot q^6+a\cdot q^5+a\cdot q^4+a\cdot q^3+a\cdot q^2+a\cdot q \\ a=10000\mathrm{/}(q^{10}+q^9+q^8+q^7+q^6+q^5+q^4+q^3+q^2+q)=10000\mathrm{/}(1.0162^{10}+1.0162^9+1.0162^8+1.0162^7+1.0162^6+1.0162^5+1.0162^4+1.0162^3+1.0162^2+1.0162)=914.43\text{ Eur} \end{gathered}$$

Try another example

Related math problems and questions:

• Deposit
  If you deposit 719 euros at the beginning of each year, how much money we have at 1.3% (compound) interest after 9 years?
• Account operations
  My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
• Annual pension
  Calculate the amount of money generating an annual pension of EUR 1000, payable at the end of the year and for a period of 10 years, shall be inserted into the bank to account with an annual interest rate of 2%
• Annual interest
  A loan of 10 000 euro is to be repaid in annual payments over 10 years. Assuming a fixed 10% annual interest rate compounded annually, calculate: (a) the amount of each annual repayment (b) the total interest paid.
• Profitable bank deposit 2012
  Calculate the value of what money lose creditor with a deposit € 9500 for 4 years if the entire duration is interest 2.6% p.a. and tax on interest is 19%. Annual inflation is 3.7% (Calculate what you will lose if you leave money lying idle at negative int
• Interest
  Calculate how much you earn for 10 years 43000 deposit if the interest rate is 1.3% and the interest period is a quarter.
• Bank
  Paul put 10000 in the bank for 6 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 3.5%, and the tax on interest is 10%.
• Slow saving in banks
  How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?
• Combined interest
  Combined interest: Carol has deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. The money was put into the account 5.5.2016 and withdraw them all before Christmas 20.12.2016. How much money did she withdraw?
• The deposit
  Deposit has been placed for one year at an annual rate of 4.5%. After the added interst amount rose to € 2,612.5. Determine initial deposit.
• Five years
  Nakato Nobuki, a Japanese artist, wants to have $24,000.00 in his savings account at the end of five years. Mr. Nobuki deposits $1,500.00 annually into savings and has a balance of $8,000.00 today. What must the interest rate on the savings account be for
• Future value
  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?
• Deposit is pesos
  Sally deposits Php.22,000 in her savings account. If the bank pays 1.5% interest per year, how much will she receive at the end of the year?
• 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.
• Bank deposit
  Ms Jana after the withdraw amount of 2,500 euros after year saving in bank. What was her deposit if the interest rate was 2.5% p.a..
• Compound interest
  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?
• Volume of wood
  Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?