1. Compute the equal monthly payments and the cost of financing on a 25-year mortgage. The cash value of the house today is $500,000. You are paying monthly at a fixed rate of 6% per year compounded monthly. You are required to downpay 10% of the house value at the beginning. At the ending of this mortgage you plan to pay off the house completely. The first monthly payment is one month from the start of the mortgage.
2. Compute the equal monthly payments and the cost of financing on a 10-year mortgage. The cash value of the house today is $500,000. You are paying monthly at a fixed rate of 6% per year compounded daily. You are required to downpay 10% of the house value at the beginning. At the end of the mortgage you plan to pay off one-half of the today's cash value of the house. The first monthly payment is one month from the start of the mortgage.
3. Compute the today's cash value of a car that can be leased with $5000 down, bi-weekly payments of $199 over 4 years and a buy-back value of $15,000 at the end of the lease if the financing interest rate is 4.9% per year compounded daily. First bi-weekly payment is two weeks after the beginning of the lease.
4. Find out the costs of financing for two schedules of monthly payments on a 25-year mortgage. The cash value of the house today is $500,000. You are paying monthly at a fixed rate of 6% per year compounded annually, and downpay 10% of the house value at start. At the end of this mortgage you plan to pay off the house completely. The first monthly payment is 1 month from start.
Schedule A: you ramp down the monthly payments so that they diminish with time, by 0.5% per month compounded monthly.
Schedule B: you keep the monthly payments equal.
5. Evaluate the probability of 10 or more customers arriving in 2 hours if on average 7 customers arrive within one hour. Customers arrive independently.
6. Compute the range of monthly financing rates for which the schedule of monthly cash flows is profitable:
Month Cash Flow, $
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0 -10,100
1 +23,000
2 -13,000
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7. Find the probability of 6 successes and 6 failures to occur, in any order, if the probability of a success is 0.7 and of a failure is 0.3; results of each trial are independent of each other.
8. Using the table below, compute the amount of overall increase of your purchasing power over the period of 5 years given the annual investment return rates and annual inflation rates:
Year Investment Return Rate, % Inflation, %
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1 5 2
2 10 9
3 15 20
4 10 10
5 15 10
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