Robert has struck an agreement to buy his dad’s car. The sale takes place when Robert can pay the depreciated value of the car: Quantitative method in Business Assignment, SBT, Australia

• Robert has struck an agreement to buy his dad’s car. The sale takes place when Robert can pay the depreciated value of the car.

The car is valued at $28,000 today but loses 3% in value each month due to depreciation.

Robert starts a regular savings plan to buy the car and plans to invest $100 at the end of each month into an account that earns him 2% per month.

1. Calculate, to the nearest month, how long Robert must wait before he can buy the car?
2. Robert wants to have the car in three years and so he searches for a bank account that can pay a higher interest rate. What is the minimum rate he must look for to achieve his goal?
3. The best offer rate Robert can find is 3.5% per month, but he is determined to get the car. He plans to revise the amount of his monthly savings. Calculate the minimum this has to be to achieve his goal.

• In a fishpond, 1200 salmon are introduced for farming/harvesting. Each year the number of salmon increases by 30% before 400 are harvested.

1. Formulate this information into a finite-difference model, clearly explaining all variables used.
2. Compute the first 10 years of the salmon numbers. What do you notice?
3. Suppose now, that only 300 are harvested each year. Compute the first 10 years again and compare the results.
4. Solve the differential equation in terms of H, the number that should be harvested to keep the numbers from either going to zero or growing without bound. Calculate the value of H for this.