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- An individual makes rental payments of $1,200 per month and wants toknowthe present value of their annual rentals over a 12-month period. The paymentsare made at the start of each month. The current interest rate is 8%per annum.You have decided to endow your favorite university with a scholarship.It is expected to cost $15,000 per year to attend the university intoperpetuity. You expect to give the university the endowment in 5 yearsand will accumulate it by making equal annual (end-of-year) depositsinto an account.The rate of interest is expected to be 8% for all future time periods.a) How large must the endowment be?b) How much must you deposit at the end of each of the next 5 yearsto accumulate the required amount?$1000 is deposited into a 9% account today. At the end of 2 yr, another $3000 will be deposited. In 5 yr, a $4000 purchase will be made. Approximately how much will be left in the account 1 yr after the purchase?
- Farmer Sam's farm is in a hilly section of the state. Erosion has always been a problem, but in recent years it has caused a decline in yields. Over the next 5 years, he expects that his profits per acre will fall as seen in the following table. He is considering putting in terraces, which would stop the erosion and hold profits at $10 per acre. If he doesn't pay for terracing, he will put the money in the bank and earn 3% interest per year. What is the present value of profits per acre with and without terracing? Show your math or spreadsheet calculations for each of the 5 years. Year Profits per Acre WITHOUT Terracing Profits per Acre WITH Terracing $10 1 $10 $9 $10 3 $8 $10 4 $7 $10 $6 $10A young professional wishes to have $890000 in her retirement account. Its current value is $13000. She invests $900 monthly in the account which earns 9.7% annually. Find the number of payments needed to reach her goal.You buy a $200,000 house using a 30-year mortgage. At the end of the 15th year you will need to replace the roof and pay $15,000. At the end of the 10th and 20th year, you will need to replace the hot water heater and pay $2,000 each time. If i-6%, what is the equivalent uniform annual cost of owning the house? nid w
- Arithmetic Gradients 4- Assume an 8% interest rate and find S, T, and X. 52 1800 A 800 1200 600 400 600 200 0-1-2–3- 0-1- (a) S = value at t = 0 (b) T = uniform value for 5 periods 600 450 300 150 (c) X = value at t = 01. You have just been elected into the “Society of HonorableEngineers.” First-year dues are waived in honor of your election.Thus, your first-payment of $200 is due at the end of the year, andannual dues are expected to increase 3% annually. After 40 years of paying dues you become a life member and pay no more dues.Instead of paying annual dues, however, you can pay a one-time$2000 life membership fee. (a) Show the equation for determining the rate of return for buying alife membership. (b) What is the rate of return?What is the present value of the amount received after 5 years, when the amount is $200, and the rate of interest is 5%? a) 121.34 b) 176.41 c) 156.71 d) 132.62
- Demand for a new product will decline as competitors enter the market. If interest is 10%, what is an equivalent uniform value?A firm is considering which of twodevices to install to reduce costs. Both devices have useful lives of 5 years and no salvage value. Device A costs $10,000 and can be expected to result in $3000 savings annually. Device B costs $13,500 and will provide cost savings of $3000 the first year but will increase $500 annually, making the second-year savings $3500, the third-year savings $4000, and so forth. For a 7% MARR, which device should the firm purchase?You decide to put $500 in a retirement account every 6 months for the next ten years. Assuming that the account pays 5% interest and compounds semi-annually, how much will you have at the end of ten years?
