A loan was made at a monthly rate of $i\%$, using compound interest, in eight fixed and equal installments of $P$.
The debtor has the possibility of paying off the debt early at any time, paying for this the present value of the remaining installments. After paying the $5^{\text{th}}$ installment, he decides to pay off the debt when paying the $6^{\text{th}}$ installment.
The expression that corresponds to the total amount paid for the loan settlement is\\
(A) $P \left[ 1 + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) } + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) ^ { 2 } } \right]$\\
(B) $P \left[ 1 + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) } + \frac { 1 } { \left( 1 + \frac { 2i } { 100 } \right) } \right]$\\
(C) $P \left[ 1 + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) ^ { 2 } } + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) ^ { 2 } } \right]$\\
(D) $P \left[ \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) } + \frac { 1 } { \left( 1 + \frac { 2i } { 100 } \right) } + \frac { 1 } { \left( 1 + \frac { 3i } { 100 } \right) } \right]$\\
(E) $P \left[ \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) } + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) ^ { 2 } } + \frac { 1 } { \left( 1 + \frac { i } { 100 } \right) ^ { 3 } } \right]$