Ivan wants to buy a condominium that costs \( \$ 72,000 \). The bank requires a \( 10 \% \) down payment. The rest is financed with a 15 -year, fixed-rate mortgage at \( 3.5 \% \) annual interest with monthly payments. Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas. (a) Find the required down payment. (b) Find the amount of the mortgage. s \( \square \) (c) Find the monthly payment. s

To figure this out, let's break it down step by step! First up, let's tackle the required down payment. (a) The down payment is \( 10\% \) of the purchase price of the condominium. \[ \text{Down Payment} = 0.10 \times 72,000 = 7,200 \] So, Ivan needs to make a down payment of **\$7,200**. (b) Now, let's find out the amount of the mortgage. The mortgage amount is the total price minus the down payment. \[ \text{Mortgage Amount} = 72,000 - 7,200 = 64,800 \] Thus, the mortgage amount Ivan will need is **\$64,800**. (c) Finally, we need to calculate the monthly payment using the formula for a fixed-rate mortgage: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: \( M \) = monthly payment, \( P \) = loan principal (mortgage amount), \( r \) = monthly interest rate, and \( n \) = number of payments (months). First, let's calculate the monthly interest rate and the total number of payments. \[ r = \frac{3.5\%}{12} = \frac{0.035}{12} \approx 0.00291667 \] \[ n = 15 \times 12 = 180 \text{ months} \] Now, substituting the values into the mortgage formula: \[ M = 64,800 \times \frac{0.00291667(1 + 0.00291667)^{180}}{(1 + 0.00291667)^{180} - 1} \] Calculating \( (1 + 0.00291667)^{180} \): \[ (1 + 0.00291667)^{180} \approx 1.7137 \] Now we can plug this back in to find \( M \): \[ M = 64,800 \times \frac{0.00291667 \times 1.7137}{1.7137 - 1} \] \[ M \approx 64,800 \times \frac{0.0050074}{0.7137} \approx 64,800 \times 0.007006 = 454.61 \] Thus, the monthly payment is approximately **\$454.61**. In summary: - Required down payment: **\$7,200** - Amount of the mortgage: **\$64,800** - Monthly payment: **\$454.61**