The price of a condominium is \( \$ 110,000 \). The bank requires a \( 5 \% \) down payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortgage at \( 7.5 \% \). Use the following formula to determine the regular payment amount. Complete parts (a) through (e) below. \[ \text { PMT }=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} \] b. Find the amount of the mortgage. \( \$ 104,500 \) c. How much must be paid for the one point at closịg? \( \$ 1,045 \) (Round to the nearest dollar as needed.) d. Find the monthly payment (excluding escrowed taxes and insurance). \( \$ 731 \) (Round to the nearest dollar as needed.) e. Find the total cost of interest over 30 years. \( \$ \square \) (Round to the nearest dollar as needed.)
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Did you know that the concept of a mortgage dates back to the ancient Romans? Back then, they had a system called "hypotheca," which allowed for the securing of loans with property. Fast forward to today, mortgages are the backbone of real estate financing, making homeownership attainable for millions. It’s fascinating how historical practices have evolved into modern financial instruments we use to buy our dream homes! Now, about your total interest cost: for a 30-year mortgage of \( \$ 104,500 \) at \( 7.5\% \), the total payment over the life of the loan would be \( 731 \times 360 = \$ 263,160 \). Subtracting the principal amount \( 104,500 \) from that gives you total interest of about \( \$ 158,660 \). That's some serious cash, but it’s all part of the journey to homeownership!
