Chapter 11.2, Problem 61PPS

To determine

Find the total amount of money Daniela borrowed in 12 months.

Answer to Problem 61PPS

Total amount of money Daniela borrowed in 12 months is $2250

Explanation of Solution

Given:

Daniela borrowd some money from her parents. She agreed to pay $50 at the end of the first month and $25 more each additional month for 12 months. How much does she pay in total after the 12 months?

Concept Used:

She agreed to pay $50 at the end of the first month and $25 more each additional month for 12 months.

First term = $50 , common difference : d = $25 and number of terms = 12

  $a_1=50;d=25;n=12;\text{Find}{\text{S}}_{12}$

Calculation:

  $a_1=50;d=25;n=12;\text{Find}{\text{S}}_{12}$

  $\begin{array}{l}{a}_1=50;d=25;n=12;\text{Find}{\text{S}}_{12}\\ {\text{S}}_n=\frac{n}{2}[2·a_1+(n-1)·d]\\ {\text{S}}_{12}=\frac{12}{2}[2·50+(12-1)·25]\\ {\text{S}}_{12}=6·[100+275]=6·375\\ {\text{S}}_{12}=2250\end{array}$

Thus, total amount of money Daniela borrowed in 12 months is $2250.