If you deposit $100 in the account at the end of each year and the account earns 6% interest, compounded annually. You will have $1,790.85 in your saving account in ten years.
The formula to calculate compound interest is:
[tex]A = P (1+ r/n)^{nt}[/tex]
A is the total value for the future investments or the total balance. P is the principal amount or the value of investment.
r is the annual rate interest. n is the number of times the interest is compounded in each year. it is also known as compound frequency.
T is the total number of years that the money will be invested.
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If you deposit $1000 at the end of each year at 6% interest rate while compounded annually, after ten years you will have $ 13,180.79
If you deposit $1000 at the end of each year at a 6% interest rate then you will get $13,180.79 after ten years. It is noted that in this question the initial investment is 0.
Compounding: First we need to know what is compounding. It is the interest that is automatically added to your balance in your standard bank account. You earn interest on that interest in the future years. This interest of reinvestment in the original deposit is called compounding.
Now we need to calculate the compound interest.
Here it is noted that there are two different formulas are used to calculate the future value of deposit. If you deposit the money at the end of period, then the ordinary annuity formula is used. If you deposit at the beginning of deposit period then annuity due formula is used.
In this question, we will use the ordinary annuity to calculate the future value of the deposits.
[tex]FV_{A} = Pmt[\frac{(1+i)^n -1)}{i}][/tex]
Where [tex]FV_{A}[/tex] = future value of an ordinary annuity
[tex]P_{mt}[/tex] = deposit each period
i= interest rate in decimal form
n= number of (compounding periods) years
[tex]FV_{A} = 1000[(1+0.06)^{10} -1)/10][/tex]
[tex]FV_{A} = 1000[(1+0.06)^{10} -1)/0.06][/tex]
[tex]=1000[1.06^{10} -1)/0.06][/tex]
=1000[(1.7908 – 1)/0.06]
=1000(0.7908/0.06)
=1000(13.1879)
= $13180.79
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