Chapter 12.4, Problem 22E

To determine

To find: The price of the ring.

Answer to Problem 22E

The price of the ring is $341.24.

Explanation of Solution

Given:

Mortgage Payment = $30

Interest Rate = 10% per year (or 0.8333% monthly)

Number of Payments = 1 year (or 12 months)

Formula:

$A_P=R\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right]$

Here,

A_P = Present Value of Annuity

R = Periodic Payment

i = Interest Rate

n = Number of Years

Mortgage: A mortgage is considered as a guarantee or a security for a loan on property or real estate. The mortgagor enters into an agreement with a mortgagee to receive loan amount initially and repay the loan during a specified time period and interest rate.

Calculation:

The price of the ring is calculated by adding 1 plus interest rate to the power minus number of years and subtracting the result by 1 and dividing the whole result by interest rate and multiplying the final result with periodic payments.

Calculate the price as follows.

$\begin{array}{c}{A}_P=R\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right]\\ =\$30\times \left[\frac{1-{\left(1+\left(\frac{10\%}{12}\right)\right)}^{-12}}{\left(\frac{10\%}{12}\right)}\right]\\ =\$30\times \left[\frac{1-{\left(1+0.8333\%\right)}^{-12}}{0.8333\%}\right]\\ =\$30\times \left[\frac{1-0.9052}{0.8333\%}\right]\end{array}$

$\begin{array}{l}=\$30\times \left[\frac{0.0948}{0.8333\%}\right]\\ =\left[\$30\times 11.3745\right]\\ =\$341.2353or\$341.24\end{array}$

Therefore, the price of the ring is $341.24.