Compunded annually problem: ...If a principal amount of $5,000 grows to $6384.50...

[Joesadlife]

Suppose that an amount of money, called the principal P, is deposited into an account that earns interest at a rate r, compounded annually. In two years that investment will grow to an amount A.

a. state the equation for this problem. (Before i move onto step b i need to know if this formula is correct? Any help would be appreciated. Is there a common formula for these type of problems that i can use?)
My result A=P*r^t

b. If a principal amount of $5,000 grows to $6384.50 in two years, what is the interest rate?

 

[Deleted member 4993]

Suppose that an amount of money, called the principal P, is deposited into an account that earns interest at a rate r, compounded annually. In two years that investment will grow to an amount A.

a. state the equation for this problem. (Before i move onto step b i need to know if this formula is correct? Any help would be appreciated. Is there a common formula for these type of problems that i can use?)
My result A=P*r^t ........... Incorrect

b. If a principal amount of $5,000 grows to $6384.50 in two years, what is the interest rate?

A = P * (1 + r)^t

 

[Dale10101]

What is happening?

Suppose that an amount of money, called the principal P, is deposited into an account that earns interest at a rate r, compounded annually. In two years that investment will grow to an amount A.

a. state the equation for this problem. (Before i move onto step b i need to know if this formula is correct? Any help would be appreciated. Is there a common formula for these type of problems that i can use?)
My result A=P*r^t

b. If a principal amount of $5,000 grows to $6384.50 in two years, what is the interest rate?

Suppose you start with P dollars and you keep it in the bank with the agreement that on the first day of the next year P will be increased by r = 10% = .1 so that P becomes A₁ = P(1.10). Now suppose you keep A₁ in the bank for another full year, then A₂ = A₁(1.10) = (P(1.10))(1.10) = P(1.10)² . By the same logic A₃ = P(1.10)³ ... and so on.

The overall insight is that the increase in P is calculated as a function of counting the number of times you are going to increase P not by a set amount but by a set factor (1 + r). I find that understanding this allows one to write out A = P * (1 + r)^t with an understanding of its meaning. Of course, one must then be able to manipulate the algebra to solve for any of A, P, r, or t as a function of the remaining variables for different forms of the same fundamental formula.

In this light consider the meaning of the formula that you have written, would you be satisfied with the result if this was the deal that your bank was offering you?

 

[Harry_the_cat]

T

 

[Harry_the_cat]

Suppose that an amount of money, called the principal P, is deposited into an account that earns interest at a rate r, compounded annually. In two years that investment will grow to an amount A.

The key word in the sentence above is compounded. You need the compound interest formula as given in the posts above. The formula you wrote is for simple interest. Make sure you know the difference.
Meow!

 

[Harry_the_cat]

Remember Thomas Hewitt Edward Cat ?

That's where I got my middle name from. Probably a distant ancestor - he'd used up his nine lives.
Meow!