Answer To: ST ADME62 @ chenzeb x @ chenzebi x x | © Wod|Mc x | 55 Sonintoy x | © Word|mi...
Prince answered on Apr 04 2023
Question: 1. You have received $100,000 from your grandparents to be used for your graduate studies. You plan to start a program in 5 years. You can invest the money at 6% interest, compounded annually. How much will you have in 5 years?
Solution: 1
FV = PV x (1 + r)n
FV = $100,000 * (1 + 0.06)5
FV = $100,000 * 1.3382
FV = $133,820
Therefore, in 5 years, the investment will grow to $133,820 at 6% interest, compounded annually.
Question: 2. Mobile Health needs to replace its mobile medical unit to continue providing diagnostic services and preventative medicine to city residents. The van costs $120,000, and a bank is willing to lend the nonprofit the money at a 6% interest rate for 5 years. Payments are due at the end of each month, and interest is compounded monthly. How much should you budget for the monthly payment?
Solution: 2
To calculate the monthly payment for a loan, we can use the formula for the present value of an annuity:
PMT = PV * (r/m / (1 - (1 + r/m)^(-m*n)))
PMT = $120,000 * (6%/12/ (1 - (1 + 6%/12)^(-5*12)))
PMT = $2,319.94
Therefore, the monthly payment should be approximately $2,319.94.
Question 3. The Department of Corrections (DOC) needs to replace two of its prison transport buses. There are two companies that have a track record of making reliable vehicles, and both make a bus that meets the needs of the department. The DOC pays an 8% interest rate on money it borrows. The bus from Company A has a purchase price of $105,000 and a 10-year service life expectancy, and it averages $2,000 per year in maintenance costs. The bus from Company B has a purchase price of $110,000 and a 10-year service life expectancy, and it averages $1,500 per year in maintenance costs. Which bus should the Department of Corrections select?
Solution: 3
To determine which bus the Department of Corrections should select, we need to consider the present value total cost of each bus over its 10-year service life. This includes both the purchase price and the annual maintenance costs.
Company A:
Year
Particular
Amount
Discounting Factor @ 8%
Present Value
0
Purchase Price
$105,000.00
1.0000
$105,000.00
1
Annual maintenance costs
$2,000.00
0.9259
$1,851.85
2
Annual maintenance costs
$2,000.00
0.8573
$1,714.68
3
Annual maintenance costs
$2,000.00
0.7938
$1,587.66
4
Annual maintenance costs
$2,000.00
0.7350
$1,470.06
5
Annual maintenance costs
$2,000.00
0.6806
$1,361.17
6
Annual maintenance costs
$2,000.00
0.6302
$1,260.34
7
Annual maintenance...