Question

Which of the following is missing in the explicit formula for the compound interest geometric sequence below?

Answer 1

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:

$Pn=P1(1+i)^{(n-1)}$

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

$P2=10(1+(5/100))$

$P2=10(1+(5/100))^{(2-1)}$

$P2=10(1+(5/100))^{(1)}$=10,5

n=3 year

$P3=10(1+(5/100))*(1+(5/100))$

$P3=10(1+(5/100))^{(3-1)}$

$P3=10(1+(5/100))^{(2)}$=11.025

n=4 year

$P4=10(1+(5/100))*(1+(5/100))*(1+(5/100))$

$P4=10(1+(5/100))^{(4-1)}$

$P4=10(1+(5/100))^{(3)}$= 11.57625