# Dan Hercher bought a home in Homewood, Illinois, for $230,000. He put down 20% and obtained a...

## Question:

Dan Hercher bought a home in Homewood, Illinois, for $230,000. He put down 20% and obtained a mortgage for 25 years at 8%. What is the total interest cost of the loan?

## Annuity Payments:

A substantial loan or mortgage borrowed by an individual or a firm is usually repaid by making equal monthly installments for a certain time horizon. The value of the monthly installments is primarily governed by the relevant interest rate.

## Answer and Explanation: 1

The calculated value of the total interest cost of the loan is **$243,506.33**.

The amount of principal for the mortgage is given by:

- = Purchase price of the car - down payment
- = Purchase price - (20% * purchase price)
- = $230,000 - (20% * $230,000)
- = $230,000 - $46,000
- = $184,000

The monthly interest rate is given by:

- = Annual interest rate / number of months in a year
- {eq}= \dfrac{8\%}{12} {/eq}

- = 0.66%

The formula for monthly payment on mortgage is given as:

{eq}R\, = \dfrac{i}{1\, -\, \left ( 1\, +\, i \right )^{-n}}\times P {/eq}

Where;

R = monthly payment

i = interest rate = 0.666% (or 0.0067)

P = Borrowed principal amount = $184,000

n = number of payments = Number of years * number of months in a year = 25 * 12 = 300

{eq}R\, = \dfrac{0.0067}{1\, -\, \left ( 1\, +\, 0.0067 \right )^{-300}}\times 184,000 {/eq}

{eq}R = $1,425.02 {/eq}

The total interest cost of the loan is given by:

{eq}\begin{align*} &= (\text{Monthly mortgage payment} \times \text{Number of payments}) - \text{borrowed principal amount}\\[0.3 cm] &= ($1,425.02 \times 300) - $184,000 \\[0.3 cm] &= $427,506.33 - $184,000 \\[0.3 cm] &= $243,506.33 \end{align*} {/eq}

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Chapter 2 / Lesson 7An annuity is a fixed amount of income paid at regular intervals, such as monthly or quarterly. Learn the definition and formula for annuity, review examples of annuities, and understand how to determine the value of annuities.