you deposit $1000 at 3% per year.what is the balance at the end of one year,and what is the annual yield,if the interest.Please help solve the problem.
Simple interest?
Compounded annually?
Compounded quarterly
Compounded daily
John,George,Mike or Lucky,
This is the same type of question as your previous question:
http://www.jiskha.com/display.cgi?id=1302748623
Study the previous response carefully and you will get the answer for this one easily.
If you need further help, post.
This one is qt different..i need more help..Thanks!
For simple interest, and compounded yearly, at the end of one year, the interest is the same, as there is only one period.
interest rate = 1.03
Balance = PRN = 1000*1.03*1 = $1030
Interest = balance - principal = 1030-1000=$30
Principal = P = $1000
Compound interest
Compounded annually:
balance = PRn = 1000*1.03^1 = $1030
Interest = 1030-1000=$30
Compounded quarterly:
n = 12months/3months = 4
R = 1+0.03/4 = 1.0075
balance after 1 year
= PR^n
interest = PR^n-P
Compounded daily:
n=365
R=1+0.03/365
balance after 1 year
= PR^n
interest = PR^n-P
Thank you very much for your help!
PR^n-P
To solve this problem, we need to calculate the balance at the end of one year and the annual yield for each scenario: simple interest, compounded annually, compounded quarterly, and compounded daily.
1. Simple Interest:
The formula for simple interest is: I = P * r * t
Where:
- I is the interest earned
- P is the principal (initial deposit)
- r is the interest rate per period
- t is the number of periods
In this case, P = $1000, r = 3% = 0.03, and t = 1 year.
I = 1000 * 0.03 * 1 = $30
Balance at the end of one year = P + I = $1000 + $30 = $1030
Annual Yield = I / P = $30 / $1000 = 0.03 or 3%
2. Compounded Annually:
For compound interest, the formula is: A = P * (1 + r)^n
Where:
- A is the final balance
- P is the principal (initial deposit)
- r is the interest rate per period
- n is the number of compounding periods (in this case, 1 year)
In this case, P = $1000, r = 3% = 0.03, and n = 1
A = 1000 * (1 + 0.03)^1 = $1030
Balance at the end of one year = $1030
Annual Yield = (A - P) / P = ($1030 - $1000) / $1000 = 0.03 or 3%
3. Compounded Quarterly:
For quarterly compounding, the interest rate and number of periods need to be adjusted accordingly.
- r = 3% / 4 = 0.0075 (quarterly interest rate)
- n = 1 * 4 = 4 (number of quarterly periods in one year)
A = 1000 * (1 + 0.0075)^4 = $1030.19 (rounded to two decimal places)
Balance at the end of one year = $1030.19
Annual Yield = (A - P) / P = ($1030.19 - $1000) / $1000 = 0.03019 or 3.019%
4. Compounded Daily:
For daily compounding, the interest rate and number of periods need to be adjusted accordingly.
- r = 3% / 365 = 0.00008219 (daily interest rate)
- n = 1 * 365 = 365 (number of daily periods in one year)
A = 1000 * (1 + 0.00008219)^365 = $1030.45 (rounded to two decimal places)
Balance at the end of one year = $1030.45
Annual Yield = (A - P) / P = ($1030.45 - $1000) / $1000 = 0.03045 or 3.045%
To summarize:
- Simple Interest:
- Balance after one year: $1030
- Annual Yield: 3%
- Compounded Annually:
- Balance after one year: $1030
- Annual Yield: 3%
- Compounded Quarterly:
- Balance after one year: $1030.19
- Annual Yield: 3.019%
- Compounded Daily:
- Balance after one year: $1030.45
- Annual Yield: 3.045%