you have deposited 1000 dollars in your savings account with n annual interest rate of 4 percent compounded monthly. how much money are you going to have in your account after six months?

[(1+ 0.04/12)]^6 x 1000 = ??

is the answer 1020.164?

You got it.

well theres another part of it if you could help me with.

in the same problem find the effective interest rate after six months?

The effective interest rate is what the annual rate would be if the compounding continued at that rate.
Thus for this problem divide the rate by 12 like you did and use 12 for the number periods intead of 6 like this
1000*(1 + .04/12)^12=Amount
Subtract 1000 from that amount and divide it by 1000. That will give the effective rate and it should be slightly greater than .04

it the answer .041

It's very close to that. I got 0.0407415
However I think they want the rate based on the 6 month or 1/2 year amount. I'm not sure what your instructions were asking for.

I may've done that incorrectly. If yoy take the 1020.16 and subtract 1000 = 20.16 and divide that by 1000 you get
.0216 for 6 months, so the effective annual rate based on that is 2*.0216=.0432 since 6 months = 1/2 year.

ok thanks alot roger

If you check this problem again I may still have the wrong formula.
The formula for effective rate I found is (1+ i/n)^n-1
For this problem i=.04 and n=6 so effective rate should be 0.04067
I hope you check this problem again. Sorry about that. I haven't worked the formula for some time, so that's why I deciced to check it again.

Let me work an example so you can see how the calculations are done.
The formula is A=P*(1+r)^n where P is the initial amount, r is the rate expressed as a decimal and n is the number of periods in the compounding period.
For this problem P=1000, r=.04 and n=6. However, the interest is being compounded monthly so we need to divide the .04 by 12 so r=.04/12
Here is an example:
Suppose the amount were P=1200. r=.05 and n=6 and the interest is compounded monthly as it is for this problem.
The monthly interest rate would be r=.05/12=0.00416667
Then A=1200*(1+0.00416667)^6 and A=1230.31
In your problem substitute P=1000 for 1200, r=.0033333 and do the calculations similar to the ones I did.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    a woman puts $580 into a savings account for one year. the rate of interest on the account was 6 1/2%. How much interest for the year in dollars and cents?

  2. math

    Yvonne put $4,000 in a savings account. At the end of 3 years, the account had earned $960 in simple interest. A. how much does she have in her account at the end of 3 years? B. at what annual simple interest rate did the account

  3. pre-algebra

    You split $1500 between two savings accounts. Account A pays annual 5% interest and Account B pays 4% annual interest. After one year,you have earned a total of $69.50 in interest. How much money did you invest in each account?

  4. simple interest

    A total of $8000 is deposited into two simple interest accounts. On one account, the annual interest rate is 10%, while on the second account the annual simple interest rate is 12%. How much should be invested in the 10% account

  1. algebra 2

    You are depositing $1000 in a savings account at 6% annual interest rate, compounded continuously. What will the balance be after 5 years? Round your answer to the nearest hundredth.

  2. Math

    A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of the 10 years, how much money will be in the savings account?

  3. Math

    Suppose a deposit of $3,500 in a savings account that paid an annual interest rate r (compounded yearly) is worth $3,910 after 2 years. Using the formula A=P(1+r)^t, we have 3,910=3,500(1+r) ^2Solve for r to find the annual

  4. Math help! Check my answers ASAP!

    1. Which graph most likely describes the distance a person walks in a 24-hour period? (1 point) a. Graph IV** b. Graph II c. Graph I d. Graph III 2. A car traveling at 25 mi/h accelerates to 48 mi/h over the first 5 seconds. It

  1. differential equation

    If P(t) is the amount of dollars in a savings bank account that pays a yearly interest rate of r% compounded continuously ,then dP/dt=(r/100)(P) , t in years . Assume the interest is 5% annually ,P(0)=$1000 ,and no monies are

  2. algebra

    A total of $6200 is deposited into two simple interest accounts. On one account the annual simple interest rate is 2%, and on the second account the annual simple interest rate is 4%. The amount of interest earned for 1 year was

  3. mathematics

    Marsha deposited $10,000 into a savings account 3 years ago. The simple interest rate is 3% how much money did Marsha earn in interest

  4. math

    Mr. Flores opened an account with a deposit of $5,000 The account earned annual simple interest. He did not make any additional deposits or withdrawals. At the end of 4 years, the balance of the account was $6,500. What is the

You can view more similar questions or ask a new question.