Calculating Interest and Balances in Simple Savings Accounts

[mathdad]

Corey deposited 1,500 in a savings account that earns simple interest at 5.75 percent. What is the balance in his account at the beginning of the
third quarter?

a. 1,556.78
b. 1,528.13
c. 1,543.13
d. 1,612.50

When I multiply 1500 by 0.0575 and add to 1500, the answer is different than those listed.

 

[MarkFL]

In order to get one of the options listed, we have to assume that interest is compounded every 2 quarters (half a year), and so at the end of one compounding period, we have:

\(\displaystyle A=1500\left(1+\frac{0.0575}{2}\right)\approx1543.13\)

 

[mathdad]

In order to get one of the options listed, we have to assume that interest is compounded every 2 quarters (half a year), and so at the end of one compounding period, we have:

\(\displaystyle A=1500\left(1+\frac{0.0575}{2}\right)\approx1543.13\)

I see that you decided to use a formula. What if you did not know this formula for compounding interest? How can you solve this problem using just arithmetic skills or is that even possible?

 

[MarkFL]

I see that you decided to use a formula. What if you did not know this formula for compounding interest? How can you solve this problem using just arithmetic skills or is that even possible?

It may appear that I've simply used a formula, but I really just used a factorization and the fact that the interest rate (assumed to be an annual rate) must be divided by the number of times the compounding takes place annually.

In my opinion, this problem is poorly worded, as it requires too many assumptions to be made on the part of the reader. :)

 

[mathdad]

Most word problems are poorly worded.

 

[MarkFL]

Most word problems are poorly worded.

Without citing some sound statistical study of the quality of word problems in general, I suppose we can only state what we feel from our own experience, and while I have encountered what I felt were poorly worded problems, I would have to say those are in the minority. I am sure there are singular sources for problems where the majority are poorly worded, but from my experience, overall the majority of problems I have seen from a large variety of sources combined as a whole, the majority seem to be worded well. :)

 

[Wilmer]

Most word problems are poorly worded.

Well, best thing to do is TELL YOUR TEACHER :)

 

[MarkFL]

Well, best thing to do is TELL YOUR TEACHER :)

Uh oh...(Tmi) (Bandit) (Wasntme)

 

[mathdad]

Well, best thing to do is TELL YOUR TEACHER :)

What teacher? I'm a middle-aged man who loves math.

- - - Updated - - -

Uh oh...(Tmi) (Bandit) (Wasntme)

The joke's on him. LOL.

 

[mathdad]

Without citing some sound statistical study of the quality of word problems in general, I suppose we can only state what we feel from our own experience, and while I have encountered what I felt were poorly worded problems, I would have to say those are in the minority. I am sure there are singular sources for problems where the majority are poorly worded, but from my experience, overall the majority of problems I have seen from a large variety of sources combined as a whole, the majority seem to be worded well. :)

I think the best word problems are the trigonometry right triangle, law of sines, and law of cosines. The GED and ASVAB applications are also interesting. Algebra 1 and 2 word problems are good. SAT applications are horrific, to say the least.

 

[HallsofIvy]

Corey deposited 1,500 in a savings account that earns simple interest at 5.75 percent. What is the balance in his account at the beginning of the
third quarter?

a. 1,556.78
b. 1,528.13
c. 1,543.13
d. 1,612.50

When I multiply 1500 by 0.0575 and add to 1500, the answer is different than those listed.

Assuming that this is 5.75% annual interest, and interest is, by law in the United States, stated annually, the interest for a full year would be 1500(0.0575)= 86.25. For two quarters, half a year, the interest would be 43.13. That gives (c), 1,543.13.

"Compound interest" does not apply here because the problem specifically says "simple interest"

 

[MarkFL]

Assuming that this is 5.75% annual interest, and interest is, by law in the United States, stated annually, the interest for a full year would be 1500(0.0575)= 86.25. For two quarters, half a year, the interest would be 43.13. That gives (c), 1,543.13.

"Compound interest" does not apply here because the problem specifically says "simple interest"

Yes, and I take back my statement that this problem is poorly worded. Using the simple interest formula:

\(\displaystyle A=P(1+rt)=1500\left(1+0.0575\cdot\frac{1}{2}\right)\approx1543.13\)

Sorry for the confusion. (Blush)

 

[mathdad]

Yes, and I take back my statement that this problem is poorly worded. Using the simple interest formula:

\(\displaystyle A=P(1+rt)=1500\left(1+0.0575\cdot\frac{1}{2}\right)\approx1543.13\)

Sorry for the confusion. (Blush)

I always thought that the simple interest formula is
I = prt not A = p(1 + rt).

 

[Wilmer]

Corey deposited 1,500 in a savings account that earns simple interest at 5.75 percent. What is the balance in his account at the beginning of the third quarter?

a. 1,556.78
b. 1,528.13
c. 1,543.13
d. 1,612.50

Well, IF there is absolutely no compounding,
then it's quite simple: 1500 + 1500*.0575*.5 = 1543.125,
as per choice c.

p = 1500
r = .0575
t = .5

 

[MarkFL]

I always thought that the simple interest formula is
I = prt not A = p(1 + rt).

$A$ is the amount in the account after interest has been added, whereas $I=Prt$ is only the amount of interest earned.

\(\displaystyle A=P+I=P+Prt=P(1+rt)\)

 

[mathdad]

$A$ is the amount in the account after interest has been added, whereas $I=Prt$ is only the amount of interest earned.

\(\displaystyle A=P+I=P+Prt=P(1+rt)\)

Thank you. I have been going through personal problems concerned with my recent future. I want you to continue to help me with my personal study of precalculus. Math is great but often life gets in the way.