Use the compound interest formulas a= p (1 + r/n) ^nt and a= pe ^ rt to solve the problem given. round to the nearest cent. find the accumulated value of an investment of $25,000 for 4 years at an interest rate of 5% if the money is 1. compounded semiannually; 2. compounded quarterly; 3. compounded monthly; 4. compounded continuously. (if possible, explain)

Step-by-step explanation:

We know that,

where,

A = Amount after time t,

P = Principle amount,

r = Rate of interest,

n = Number of times interest is compounded per year,

t = time period in year.

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded semiannually

Here,

P = $25,000

r = 5% = 0.05

n = 2 (as compounded semiannually)

t = 4 years

Putting the values,

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded quarterly.

Here,

P = $25,000

r = 5% = 0.05

n = 4 (as compounded quarterly)

t = 4 years

Putting the values,

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded monthly.

Here,

P = $25,000

r = 5% = 0.05

n = 12 (as compounded monthly)

t = 4 years

Putting the values,

Investment of $25,000 for 4 years at an interest rate of 5% if the money is compounded continuously.

where,

A = Amount after time t,

P = Principle amount,

r = Rate of interest,

t = time period in year.

Putting all the values,

It can be observed that, the frequent we compound the amount, the more we get.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

27 +27 or 27times 2=54

the diffrence is 0