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
430.00
1000*3/100*1=30
1000*3/100*1=30
1000*3/100*1=30
30/4=7.5
1000*3/100*1=30
30/365=0.082
To solve this problem, we need to understand the different types of interest calculations involved.
1. Simple Interest: This type of interest is calculated based on the initial principal amount and the interest rate. It does not consider compounding over time. The formula to calculate simple interest is: Simple Interest = Principal amount (P) * Interest rate (r) * Time period (t).
2. Compounded Annually: In this case, the interest is compounded once per year. This means that at the end of each year, the interest is added to the principal, and the subsequent interest calculation is done on the new total. The formula to calculate compounded interest annually is: Compound Interest = Principal amount (P) * (1 + Interest rate (r))^Time period (t).
3. Compounded Quarterly: With quarterly compounding, the interest is calculated and added to the principal four times a year. The formula to calculate compounded interest quarterly is: Compound Interest = Principal amount (P) * (1 + Interest rate (r)/4)^(4 x Time period (t)).
4. Compounded Daily: In this case, interest is compounded on a daily basis. The formula to calculate compounded interest daily is: Compound Interest = Principal amount (P) * (1 + Interest rate (r)/365)^(365 x Time period (t)).
Now, let's calculate the balance and annual yield for each scenario:
1. Simple Interest: Balance = Initial deposit + (Initial deposit * Interest rate * Time period) = $1000 + ($1000 * 0.03 * 1) = $1030. Annual Yield = Simple Interest = $1000 * 0.03 * 1 = $30.
2. Compounded Annually: Balance = Initial deposit * (1 + Interest rate)^Time period = $1000 * (1 + 0.03)^1 = $1030. Annual Yield = Balance - Initial deposit = $1030 - $1000 = $30.
3. Compounded Quarterly: Balance = Initial deposit * (1 + Interest rate/4)^(4 * Time period) = $1000 * (1 + 0.03/4)^(4 * 1) = $1030.38 (rounded to two decimal places). Annual Yield = Balance - Initial deposit = $1030.38 - $1000 = $30.38.
4. Compounded Daily: Balance = Initial deposit * (1 + Interest rate/365)^(365 * Time period) = $1000 * (1 + 0.03/365)^(365 * 1) = $1030.45 (rounded to two decimal places). Annual Yield = Balance - Initial deposit = $1030.45 - $1000 = $30.45.
Therefore, depending on whether the interest is calculated using simple interest, compounded annually, compounded quarterly, or compounded daily, the balance at the end of one year and the annual yield will vary slightly.