I need some help with these problems please.?

1. A self-employed person deposits $1,250 annually in a retirement account (called a SEP-IRA) that earns 5.5%.


a. How much will be in the account at age 62 if the savings program starts when the individual is age 50?


b. How much additional money will be in the account if the saver defers retirement until age 66 and continues the contributions until then?


c. How much additional money will be in the account if the saver discontinues the contributions at age 62, but lets it build up until retirement at age 66?


2. If a firm has $250,000 to invest and can earn 8.5%, compounded annually, how much will the firm have after two years?


3. A father has decided to set aside a one time lump sum for college that will amount to $60,000 by the time his 5 year old is 18 years old (13 years). Use 8% as the rate. Figure the dollar amount to put in the fund assuming no further investments will be made. How much must he invest right now to amount to $60,000 in 13 years?


4. You win a judgment in an auto accident for $275,000. You will immediately receive $135,000 in cash, but must pay your lawyer's fee of $91,666 out of that sum. In addition you will receive $5,500 per year for 20 years for a total of $110,000 after which the balance owed of $30,000 will be paid. If the interest rate is 7 percent, what is the current value of your settlement?


5. A firm borrows $935,000 for 7 years for a large item of equipment and installation costs. The interest rate is 7.5%. The loan requires that the interest and principal be paid in equal, annual payments that cover the interest and principal. The interest is determined on the declining balance that is owed. What are the annual payments and the amount by which the loan is reduced during the first year?


6. A company leases equipment for seven years. The equipment costs $28,000 and the owner (called the "lessor") wants to earn 9.5% on the lease. What should be the lease payments?|||Question a:





The person spends 12 years putting in 1 250 into an account with an annual return of 5.5 %.


We get $21 608.50.





Question b:





Total : 32 495.50


Additional: 32 495.50 - 21 608.50 = 10 887





Question c:





21 608.50 * (1.055^4) = 26 769.14





2.





250 000 * (1.085^2) = 294 306





3.





60 000 / (1.08)^13 = 22 061.88





4.





First payment is what it is: 135 000


Pay the fee: -91 666





Right now you have : 43 334





Then you get 5500 every year, for 20 years. Discount that year-by-year.


That sum total is worth 58 267.





So 43 334 + 58 267 = 191 601





Now the balance, that you get on year 20, discounted is worth 7 752.60 today. So add that all up and that settlement of 275 000 is worth 109 354.





5.





Year 0





Loan size: 945 000





Year 1:





Loan size: 810 000


Interest payment: 70 875





Year 2:





Loan size: 675 000


Interest payment: 60 750








Year 3:





Loan size: 540 000


Interest payment: 50 625





Year 4:





Loan size: 405 000


Interest payment: 40 500








Year 5:





Loan size: 270 000


Interest payment: 30 375





Year 6:





Loan size: 135 000


Interest payment: 20 250








Year 7:





Loan size: 0


Interest payment: 10 125





Total amortization: 945 000


Total interest payments : 283 500


Sum: 1 228 500





6.





Assuming no rest value on the lease and that the equipment is "worthless" after the seven years.


If the lessor want's a 9.8 % return after seven years. The return on his investment has to be 2 744, (i.e 9.8 % return on 28 000).





That means we have to look at the yearly return which is:





30 744 / 28 000 = (1 + X ) ^7


--%26gt; 1.098 = (1 + X ) ^7


----%26gt; (1.098)^(1/7) = 1 + X


------%26gt; 1.0134 = 1 + X


X = 0.0134 = 1.34 %





So about 376 per month!