Chapter 11.3, Problem 63PPS

(a)

To determine

Find the payments be at the end of the 10^th, 20^th and 40^th weeks.

Answer to Problem 63PPS

$11.79; $30.58; $205.72

Explanation of Solution

Given:

High Tech Electronics advertises a weekly installment plan for the purchase of a popular brand of high definition television. The buyer pays $5 at the end of first week, $5.50 at the end of 2^nd week, $6.05 at the end of third week, and so on one year.(Assume 1 yr = 52 wk).

What will be the payments be at the end of the 10^th, 20^th and 40^th weeks?

Concept Used:

Given: $a_1=5;r=\frac{5.50}{5}=1.1$

Calculation:

  $\begin{array}{l}{a}_1=5;r=1.1,n=10;\text{find}{a}_{10};a_{20};a_{40}\\ a_n=a_1·r^{n-1}[\text{nth}\text{term}\text{formula}]\\ $ a_{10}=5\cdot {(1.1)}^{10-1}=11.79$$ a_{20}=5\cdot {(1.1)}^{20-1}=30.58$$ a_{40}=5\cdot {(1.1)}^{40-1}=205.75$\end{array}$

Thus, $a_{10}=\$11.79;a_{20}=\$30.58;a_{40}=\$205.75$

(b)

To determine

Find the total cost of the TV.

Answer to Problem 63PPS

$7052.15

Explanation of Solution

Given:

High Tech Electronics advertises a weekly installment plan for the purchase of a popular brand of high definition television. The buyer pays $5 at the end of first week, $5.50 at the end of 2^nd week, $6.05 at the end of third week, and so on one year.(Assume 1 yr = 52 wk).

Find the total cost of the TV.

Concept Used:

Given: $a_1=5;r=\frac{5.50}{5}=1.1$

Calculation:

  $\begin{array}{l}{a}_1=5;r=1.1,n=52(\text{1}\text{year}\text{=}\text{52}\text{weeks});\text{find}{\text{S}}_{52}\\ {\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}\\ {\text{S}}_{52}=\frac{5(1-{(1.1)}^{52})}{1-1.1}=7052.15\end{array}$

Thus, total cost of the TV is in 1 year $7052.15

(c)

To determine

Find why the cost is found in part b not entirely accurate.

Answer to Problem 63PPS

Explanation of Solution

Given:

High Tech Electronics advertises a weekly installment plan for the purchase of a popular brand of high definition television. The buyer pays $5 at the end of first week, $5.50 at the end of 2^nd week, $6.05 at the end of third week, and so on one year.(Assume 1 yr = 52 wk).

Why the cost is found in part b not entirely accurate.

Concept Used:

Each payment made is rounded to the nearest penny, so the sum of the payments will actually be more than the sum found in part b.

Thus,