bus calc exam 2 formulas and definitions

compound interest

is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be expressed with the formula

A = P(1 + r/n)^{nt}

where A is the amount of money accumulated after n years, including interest.

p- initial value 

n- number of times that interest is compounded per year,

r- annual interest rate

t- number of years the money is invested or borrowed.

simple interest formula

A=p(1+rt)

where A is the total amount, p is the principal,

r is the annual interest rate,

t is the time in years.

compounded continously formula 

is a method of calculating interest where the interest is added to the principal continuously rather than at discrete intervals.

A = Pe^{rt},

A is the amount of money accumulated,

P is the principal,

r is the annual interest rate,

and t is the time in years.(in which growth occurs) 

Annual Percentage Yield 

(APY) is the annual rate of return on an investment, taking into account the effect of compounding interest. It is expressed as a percentage and provides a standardized measurement for comparing different financial products.

apy=(1+r/n)n-1 × 100 

where r is the nominal interest rate (decimal form) 

n is the number of compounding periods per year.

Annual percentage yield for an account with interest that is compounded continuously

is defined as the effective annual rate that results from continuous compounding. It can be calculated using the formula

APY = e^r - 1,

where r is the nominal interest rate.

derivative of ln(x)

1/x

derivative of e^x

e^x

derivative of pi

0

the limit defintion

of a derivative is the limit of the average rate of change of a function as the interval approaches zero. It is mathematically expressed as ( \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} ).

when a function is increasing the derivative is

above the x-axis

when a function is decreasing the derivative is

below the x-axis

when a function is smooth max/min the derivative is

x-intercept

when a function is concave up the derivative is

increasing slope

when a function is concave down the derivative is

decreasing slope

when a function is cubic the derivative is

a quadratic function that may have local maxima or minima.

when a function is quadractic the derivative is

a linear function that can have a constant or changing slope.

when a function is linear the derivative is

constant 

when a function is constant the derivative is

zero

when a function is exponential the derivative is

exponential

change formula

f(b)-f(a)

percentage change formula

(f(b)-f(a))/f(a) x 100

average rate of change (secant line slope) 

(f(b) - f(a)) / (b - a).

percentage rate of change 

f’(a)/ f(a) x 100