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Y Lab Assignment 10 (Question 1) Lyryx Learning Inc - Google Chrome :' lila1.lyryx.com/student-servlets/LabServlet?ccid =5376 Iyry Lab Assignment 10 (Question 1) Name: Henil Dilipbhai Unagar Date: 2024-04-14 Official Time: 19:29:18 Question 1[5 points] Alan is looking at leasing a car. Compute the purchase price given the lease information in the table below. For full marks your answer(s) should be rounded to the nearest cent. Note: The interest rate is the annual rate with monthly compounding. Purchase Price Down Payment Monthly Payment Interest Rate Term (months) Residual Value 0.00 $1,000 $468.61 5.50% 36 $11,093.67 SUBMIT AND MARK

Y Lab Assignment 1010 (Question 11) Lyryx Learning Inc - Google Chrome\newline∵ \because lila11.lyryx.com/student-servlets/LabServlet?ccid =5376 =5376 \newlineIyry\newlineLab Assignment 1010 (Question 11)\newlineName: Henil Dilipbhai Unagar\newlineDate: 2024−04−14 2024-04-14 \newlineOfficial Time: 1919:2929:1818\newlineQuestion 1[5 1[5 points]\newlineAlan is looking at leasing a car. Compute the purchase price given the lease information in the table below. For full marks your answer(s) should be rounded to the nearest cent. Note: The interest rate is the annual rate with monthly compounding.\newline\begin{tabular}{|cccccc|}\newline\begin{tabular}{c} \newlinePurchase \\\newlinePrice\newline\end{tabular} & \begin{tabular}{c} \newlineDown \\\newlinePayment\newline\end{tabular} & \begin{tabular}{c} \newlineMonthly \\\newlinePayment\newline\end{tabular} & \begin{tabular}{c} \newlineInterest \\\newlineRate\newline\end{tabular} & \begin{tabular}{c} \newlineTerm \\\newline(months)\newline\end{tabular} & \begin{tabular}{c} \newlineResidual \\\newlineValue\newline\end{tabular} \\\newline\hline 00.0000 & $1,000 \$ 1,000 & $468.61 \$ 468.61 & 5.50% 5.50 \% & 3636 & $11,093.67 \$ 11,093.67 \\\newline\hline\newline\end{tabular}\newlineSUBMIT AND MARK

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Q. Y Lab Assignment 1010 (Question 11) Lyryx Learning Inc - Google Chrome\newline∵ \because lila11.lyryx.com/student-servlets/LabServlet?ccid =5376 =5376 \newlineIyry\newlineLab Assignment 1010 (Question 11)\newlineName: Henil Dilipbhai Unagar\newlineDate: 2024−04−14 2024-04-14 \newlineOfficial Time: 1919:2929:1818\newlineQuestion 1[5 1[5 points]\newlineAlan is looking at leasing a car. Compute the purchase price given the lease information in the table below. For full marks your answer(s) should be rounded to the nearest cent. Note: The interest rate is the annual rate with monthly compounding.\newline\begin{tabular}{|cccccc|}\newline\begin{tabular}{c} \newlinePurchase \\\newlinePrice\newline\end{tabular} & \begin{tabular}{c} \newlineDown \\\newlinePayment\newline\end{tabular} & \begin{tabular}{c} \newlineMonthly \\\newlinePayment\newline\end{tabular} & \begin{tabular}{c} \newlineInterest \\\newlineRate\newline\end{tabular} & \begin{tabular}{c} \newlineTerm \\\newline(months)\newline\end{tabular} & \begin{tabular}{c} \newlineResidual \\\newlineValue\newline\end{tabular} \\\newline\hline 00.0000 & $1,000 \$ 1,000 & $468.61 \$ 468.61 & 5.50% 5.50 \% & 3636 & $11,093.67 \$ 11,093.67 \\\newline\hline\newline\end{tabular}\newlineSUBMIT AND MARK
  1. Identify Formula: First, let's identify the formula to calculate the purchase price of the car. The formula is based on the present value of an annuity due to the monthly payments, plus the present value of the residual value.
  2. Calculate PVA: The present value of the annuity (PVA) for the monthly payments can be calculated using the formula: PVA=PMT×[1−(1+r)−nr]PVA = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right], where PMTPMT is the monthly payment, rr is the monthly interest rate, and nn is the total number of payments.
  3. Convert Interest Rate: Convert the annual interest rate to a monthly rate by dividing by 1212: 5.50%/12=0.4583%5.50\% / 12 = 0.4583\% per month.
  4. Plug Values into Formula: Convert the monthly interest rate to a decimal for the formula: 0.4583%=0.0045830.4583\% = 0.004583.
  5. Calculate PVA: Now, plug the values into the PVA formula: PVA=$468.61×[1−(1+0.004583)−360.004583]PVA = \$468.61 \times \left[\frac{1 - (1 + 0.004583)^{-36}}{0.004583}\right].
  6. Find Value: Calculate the present value of the annuity: PVA = (\$)\(468.6161 \times \left[\frac{11 - (11 + 00.004583004583)^{−36-36}}{00.004583004583}\right] = (\$)\(468\).\(61\) \times \left[\frac{\(1\) - (\(1\).\(004583\))^{\(-36\)}}{\(0\).\(004583\)}\right].
  7. Substitute Value: Use a calculator to find the value of \((1.004583)^{-36}\): \((1.004583)^{-36} \approx 0.8424\).
  8. Complete Calculation: Substitute the value back into the PVA formula: \(PVA = \$468.61 \times \left[\frac{1 - 0.8424}{0.004583}\right] = \$468.61 \times \left[\frac{0.1576}{0.004583}\right].\)
  9. Calculate PV: Complete the calculation for the present value of the annuity: \(PVA = ( ext{ extdollar})\(468\).\(61\) \times \(34\).\(3869\) \approx ( ext{ extdollar})\(16\),\(116\).\(14\).
  10. Plug Values into Formula: Next, calculate the present value of the residual value (PV) using the formula: \(PV = \frac{FV}{(1 + r)^n}\), where \(FV\) is the residual value.
  11. Calculate PV: Plug the values into the PV formula: \(PV = \frac{\$11,093.67}{(1 + 0.004583)^{36}}\).
  12. Add PV of Annuity and Residual Value: Calculate the present value of the residual value: \(PV = \frac{ ext{ extdollar}11,093.67}{(1.004583)^{36}} \approx \frac{ ext{ extdollar}11,093.67}{1.1759} \approx ext{ extdollar}9,429.57\).
  13. Calculate Purchase Price: Add the present value of the annuity and the present value of the residual value to get the purchase price: Purchase Price = \(\$16,116.14\) + \(\$9,429.57\).
  14. Add Down Payment: Calculate the total purchase price: Purchase Price = \(\$16,116.14\) + \(\$9,429.57\) \(\approx\) \(\$25,545.71\).
  15. Calculate Total Cost: Finally, add the down payment to the purchase price to get the total cost of the car: Total Cost = Purchase Price + Down Payment = \(\$25,545.71\) + \(\$1,000\).
  16. Calculate Total Cost: Finally, add the down payment to the purchase price to get the total cost of the car: Total Cost = Purchase Price + Down Payment = \(\$25,545.71 + \$1,000\).Calculate the total cost of the car: Total Cost = \(\$25,545.71 + \$1,000 = \$26,545.71\).

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