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Freshman Clinic II Engineering Economics Homework For all problems assume interest is compounded monthly. This is an individual assignment. When turning this in, please provide a cover sheet with all numerical answers listed. 1. Many furniture stores used to advertise “no payments and no interest” on larger purchases. The time frames used to range up to 3 years into the future. If you read further, however, the small print read something like “interest accrues and is compounded at a rate of 11% from the date of purchase. If the balance is not paid in full in 36 months then the total owed is the sum of the unpaid balance plus interest charges. At 36 months the interest rate will change to a competitive 18% and regular billing will apply”. Assume you have purchased a new home and wish to furnish it with $5000 in new furniture. You decide to take a “no payments, no interest” offer because you have spent all your cash on the down payment and want to keep something in the stock market and/or savings (at 5.5% annually). a. How much will you owe on the first day after the 36 months (e.g. 36 months of interest on the purchase plus the initial principal ) and what is the present value of that sum to you? b. Using the AV conversions on the FV solution to part (a), what is the monthly payment required to pay off the entire balance in 36 months beginning 36 months after the initial purchase? What is the present value of this sum? c. If your savings/stock account earns interest, how might you create your own discount and what is it’s value? 2. To purchase your new home ($336,000, Avg. home sale prince in NJ by county) you are faced with choosing a mortgage from among two options: Option 1: 30 year fixed at 5.25 % and Option 2: 15year fixed at 4.5% (TD Bank conventional rates as of 2/14/11). a. What is your monthly payment? HINT: Use the A-P formulas to pay down the balance. b. Determine the total interest paid for both loans by creating a spreadsheet that calculates the interest and principal payments for each month. The interest due is simply (annual rate)/12*(remaining principal balance). The principal payment is the (payment in part a) – (interest payment). c. Assuming a prevailing rate of 5.5%, determine the future (30 year) and present values of all interest payments (NOTE: you must convert each payment to future or present value individually). d. You are considering not buying the house at all. Determine the present and future values of all payments (principal plus interest) in both cases and a prevailing interest rate of 5.5%. Freshman Clinic II Engineering Economics Homework 3. You expect your salary at retirement to be roughly $102,000 (neglecting inflation). You wish to retire at age 66 drawing 80% of your salary at retirement from an annuity. In this arrangement, you draw money from an account where the interest earned and money withdrawn are calculated to reduce the account to zero at a specified time in the future (e.g. your death). Assume an interest rate of 5.5% prevails. a. Determine the present value lump sums required to retire if you plan to live to 67,68,… 100 years of age. Plot the results. b. Assume you will live to be 78 years of age (average for the US according to the World Health Organization). Determine the monthly contribution required to achieve the necessary lump sum if you begin saving (and compounding) monthly from age 23, 24, 25, 26,…65. Plot the results. c. You expect to receive $2032/month in retirement benefits based on your average salary throughout your working life (the average monthly social security benefit in the US is $1074 from ssa.gov). If you receive this annuity from ages 66 to 78 determine its total “present value” at your age 66 and at your age 23.