Explain the solutions and formula to be used thank you
. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $99 + $450/1 - [1 / (1 + .07/12)"20>]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $23,000 / [1 + (.07/12)]'20> = $18,654.82 The PV of the decision to purchase is:The cash flows for this problem occur monthly, and the interest rate given is the EAR. Since the cash flow occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by 12. So, the pre-retirement APR is: EAR = .10 = [1 + (APR / 12)]"2 - 1; APR = 12[(1.10)1/12 - 1]=.0957 or 9.57% And the post-retirement APR is: EAR = .07 = [1 + (APR / 12)]" - 1; APR = 12[(1.07) 2- 1] =.0678 or 6.78% First, we will calculate how much he needs at retirement. The amount needed at retiremci. . monthly spending plus the PV of the inheritance. The PV of these two cash flows is: PVA = $20,000{1 - [1 / (1 +.0678/12)12(25)]; / (.0678/12) = $2,885,496.45 PV = $900,000 / [1 + (.0678/12)]30= $165,824.26 So, at retirement, he needs:55. The payment for a loan repaid with equal payments is the annuity payment with the loan value as the PV of the annuity, So, the loan payment will be: PVA = $42,000 = C {[1 - 1/ (1 +.08)]/ .08} C= $10,519.17 The interest payment is the beginning balance times the interest rate for the period, and the principal payment is the total payment minus the interest payment. The ending balance is the beginning balance minus the principal payment. The ending balance for a period is the beginning balance for the next period. The amortization table for an equal payment is:In general, viatical settlements are ethical. In the case of a viatical settlement, it is simply an exchange of cash today for payment in the future, although the payment depends on the death of the seller. The purchaser of the life insurance policy is bearing the risk that the insured individual will live longer than expected. Although viatical settlements are ethical, they may not be the best choice for an individual. In a Business Week article (October 31, 2005), options were examined for a 72 year old male with a life expectancy of 8 years and a $1 million dollar life insurance policy with an annual premium of $37,000. The four options were: 1) Cash the policy today for $100,000. 2) Sell the policy in a viatical settlement for $275,000. 3) Reduce the death benefit to $375,000, which would keep the policy in force for 12 years without premium payments. 4) Stop paying premiums and don't reduce the death benefit. This will run the cash value of the policy to zero in 5 years, but the viatical settlement would be worth $475,000 at that time. If he died within 5 years, the beneficiaries would receive $1 million. Ultimately, the decision rests on the individual on what they perceive as best for themselves. The values that will affect the value of the viatical settlement are the discount rate, the face value of the policy, and the health of the individual selling the policy. 1. To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: 2. To find the PVA, we use the equation
