**1.**You are applying for a 30-year, fixed-rate (APR 6.50%),monthly-payment-required mortgage loan for a house that sells for $80,000 today. The mortgage bank will ask you for 20% initial down payment of the house value, and charge you an extra $3,000 closing cost(carried into loan balance and amortized later)when the loan is approved.

(a) What should be your *monthly* loan payment (assuming payment is due by the end of each month)?

(b) 10 years after buying the house, what will be the remaining *principal* balance of your loan?(Hint:For a loan or investment, the beginning balance is the same as “present value”, whereas the ending or remaining balance is the same as “future value”.And please don’t forget this is a monthly loan.)

(c) 10 yearsafter buying the house(as Part b aforementioned),the loan market rate drops from 6.50% APR to 4.50% APR, you want to refinance on the remaining loan principal balance, but the bank will charge you an extra $4,000 refinancing fee (carried into loan balance and amortized later). Would you be able, and by how much, to lower your monthly loan payment if you choose to refinance *over the remaining loan life* (i.e., instead of the extension of another 30 years)?Based on your calculation results, should you choose to refinance or not?

**2.**By the end of each year, you contributea$3,000 to your retirement fund portfolio, which on average earns an annual return of 12.5% in the financial market.Such annualcontributions continue until your retirement.

(a) 30 years later you retire, how much money do you have in your portfolio by then?

(b) For your post-retirement life (which last approximately another 20 years), every year you withdraw and spend an equal amount of annuity payment from your fund account.What would be the *annual* payment amount youspend if you do not want to leave any money to your heirs? (Hint: Even after you retire, will the financial market and your fund account retire then?That is, what will be the applicable interest rate or money growth rate for your post-retirement years?)

(c) Considering the long-term inflation rate amounts to 3.5% annually, how much money *at real purchasing power* will you actually have when you retire?How much should you withdraw and spend per year *at real purchasing power* for your post-retirement life?(Hint: Your stated “annual return of 12.5%” is just nominal in this case; just as your boss gives you an annual salary raise of 3%, but how much *real-purchasing-power* “raise” you are getting per year actually, considering the annual inflation factor?)

**6.A**

**7.**If you deposit $4,000 at the end of each of the next 20 years into an account paying 11.2 percent interest, how much money will you have in the account in 20 years? How much will you have if you make deposits for 40 years?

**8**.You want to have $90,000 in your savings account 10 years from now, and you’re prepared to make equal annual deposits into the account at the end of each year. If the account pays 6.8 percent interest, what amount must you deposit each year?

**9.**Dinero Bank offers you a $50,000, seven-year term loan at 7.5 percent annual interest. What will your annual loan payment be?

10.The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. If the recquired return on this investment is 7.2 percent, how much will you pay for the policy?

**5.A**

**6.**Assume the total cost of a college education will be $290,000 when your child enter college in 18 years. You presently have $55,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?

**7.**At 7 percent interest, how long does it take to double your money? To quadruple it?

**9.**You’re trying to save to buy a new $170,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

11.You have just received notification that you have won the $1 million first prize in the centennial liberty. However, the prize will be awarded on your 100^{th} Birthday (assuming you’re around to collect). 80 years from now. What is the present value of your windfall if the appropriate discount rate is 10 percent?

**18.**You have just made your first $4,000 contribution to your retirement account. Assuming you earn an 11 percent rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing?