MATH 2070 - Integral Applications in Finance Formulas

Constant

• R(t) = A million dollars per year

• A = profit to be invested

Linear

• Changes by the same amount every year

• Increase: R(t) = A + bt million dollars per year

• Decrease: R(t) = A - bt million dollars per year

• A = profit to be invested

• t = time (Usually in years)

• b = increase/decrease by $_ per year

Exponential 

• Changes by the same percentage every year

• Increase: R(t) = A[(100+b)/100]^t

• Decrease: R(t) = A[(100-b)/100]^t

• A = profit to be invested

• t = time (Usually in years)

• b = increase/decrease by $_ per year

Only invest a portion (p%) of their profit 

(p/100) * R(t)

Principle (T)

0 integral T: R(t) dt

Interest earned

Perpetual Income Stream

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The profit increases by 0.7 million per year

R(t) = .7t+2.5

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The proft remains the same each year, and the team invests 15% of their profit

R(t) = .15(2.5)

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The profit decreases by 12% each year, and the team invests 8% of the profit.

R(t) = .08(2.5)(.88)^t

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The profit decreases by 0.25 million per year, and the team invests 10% of the profit.

R(t) = .1(0.25t+2.5)

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The profit increases by 6% each year

R(t) = 2.5(1.06)^t

Suppose a sports team earns an annual profit of 2.5 million dollars. They invest the profit as a continuous income stream. Write the rate of flow equations:

The profit remains the same each year.

R(t) = 2.5