I. PROBLEMS.

A. We want to become millionaires. Our 10th birthday is today, and our grandparents give us $15,000, which we invest at 5% interest rate. We shall pay for a 4 year bachelor's from our pocket in 8 years at $30,000 per annum. In year 16, we take a vacation to the Greek islands, and it costs us $20,000. We put aside $3,000 per annum.
How old shall we be when we attain our goal?

B. We receive a mortgage loan for 20 years.. The mortgage rate is 6% per annum. Additionally, the monthly payment we ought to make to the bank to amortize the loan is $2, 500. Secondly, compute the remaining amount we still owe the bank, if we pay an additional single sum of $50,000 after 5 years. Thirdly, as part of this computation, find how many more months, we will pay the bank to induce the loan expire. Fourthly, if we accumulate a lot by year 10(end of the year), how much would we give additionally to the lender to eliminate the loan? Fifthly, how much is the effective annual rate?

C.1) We receive $3,000 per semester and $87,000 in 9 years from the present.
What ROR did we attain, if we now invest $4,000?

2) We buy an asset for $20,000. We receive money to the tune of ___ per month.
At the end, 4 years later, we are paid $12,000. The ROR is 10%. What was that money receipt?

D. We buy a car for $40,000. They charge us 8% annual interest. We pay the loan off quarterly. We want to know the effective annual ROR and the quarterly amount to pay off the loan in 6 years. Furthermore, if we had enough after 1 year, how much do we need to give the lender to amortize? If we gave the lender $6,000 in addition to our regular amount after 2 years, how many more payments would we need to give?

E. We want to retire in 40 years, and we shall need $45,000 income per annum during our retirement which will last 35 years. We can save $20,000 annually during the first 9 years. We estimate that from year 6 till 10 we shall return to school for a graduate degree, which will cost $30,000 yearly in actual cash flow and opportunity cost expenses. Afterward, during years 20 to 30, our father will need nursing home care for 10 years. He has to give his house and $70,000 annually to the nursing home. Furthermore, we shall buy a yacht costing $150,000 in year 40. Additionally, we'll send our niece to college which will cost $50,000 per annum for 4 years starting in year 6 from now. We would like to know what the pension fund should be to finance our retirement. Second, what annual savings should we accumulate from years 30 to 40 to be able to fund all the aforementioned expenses and our retirement. We have a discount rate of 10%.