Answer:
1+i
Step-by-step explanation:
The explicit formula for the compound interest geometric tell us: If P1 is invested at an interest rate of i per year, compounded annually, the future value Pn at the end of the nth year is:
[tex]Pn=P1(1+i)^{(n-1)}[/tex]
For example if you have $10 at 5% at an interest rate of 5% per year.
Then if you want to know the amount of money at the end of the 2, 3 and 4 year, you have:
n=1 year P1=10
n=2 year
[tex]P2=10(1+(5/100))[/tex]
[tex]P2=10(1+(5/100))^{(2-1)}[/tex]
[tex]P2=10(1+(5/100))^{(1)}[/tex]=10,5
n=3 year
[tex]P3=10(1+(5/100))*(1+(5/100))[/tex]
[tex]P3=10(1+(5/100))^{(3-1)}[/tex]
[tex]P3=10(1+(5/100))^{(2)}[/tex]=11.025
n=4 year
[tex]P4=10(1+(5/100))*(1+(5/100))*(1+(5/100)) [/tex]
[tex]P4=10(1+(5/100))^{(4-1)}[/tex]
[tex]P4=10(1+(5/100))^{(3)}[/tex]= 11.57625
