If your bank pays 5.5 percent interest on savings deposits, what is the simple interest paid in the third year on an initial $100 deposit?
What is the total amount in the account after three years?
What is the amount after three years if the interest was compounded annually?
the same as every other year: .055*100 = 5.50
100(1+.055*3) = 116.50
100(1.055)^3 = 117.42
Well, well, well, let's get jiggy with some math, shall we?
If your initial deposit is $100 and your bank pays 5.5 percent simple interest, you can calculate the interest for each year by multiplying the initial deposit by the interest rate. In this case, 5.5 percent of $100 is $5.50. So, in the first year, you'll earn $5.50 in interest.
In the second year, you'll again earn 5.5 percent interest on your initial deposit of $100. That's another $5.50 in interest.
Drumroll, please! In the third year, you'll once again earn 5.5 percent interest on your original deposit. That's another $5.50 in interest.
Adding up the interest earned in each year, you get $5.50 + $5.50 + $5.50, which equals $16.50. That's the simple interest paid in the third year.
Now, let's calculate the total amount in the account after three years. In each year, you'll be adding the interest earned to the initial deposit. So, after three years, you'll have $100 (the initial deposit) + $16.50 (the total interest earned), which equals $116.50. Voila!
Ah, but wait, there's more! If the interest is compounded annually, things get a bit fancier. With compound interest, the interest earned each year is added to the account, and then you earn interest on that interest too! It's like a never-ending spiral of growth. Unless it's your waistline after eating too much ice cream. But I digress.
To calculate the amount after three years with compounded interest, we'll use the following formula: A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the interest is compounded annually, so n = 1.
If we plug in the numbers, we have A = $100(1 + 0.055/1)^(1*3), which simplifies to A = $100(1.055)^3.
Calculating that, we get A = $100 * 1.169, which equals $116.90. So, after three years with compounded interest, you'll have $116.90 in the account.
So, to summarize:
- The simple interest paid in the third year is $16.50.
- The total amount in the account after three years with simple interest is $116.50.
- The amount after three years with compounded interest is $116.90.
Now, that's some mathematical jesting! Hope it put a smile on your face!
To calculate the simple interest paid in the third year, you would need to multiply the initial deposit by the interest rate. The formula for simple interest is:
Simple Interest = Principal (initial deposit) * Interest Rate * Time
= $100 * 0.055 * 3 (since it's the third year)
The simple interest paid in the third year would be $16.50.
To calculate the total amount in the account after three years, you would add the simple interest paid in the third year to the initial deposit. Therefore:
Total Amount = Initial Deposit + Simple Interest
= $100 + $16.50
= $116.50.
Now, if the interest is compounded annually, we can calculate the amount after three years using the formula for compound interest:
Compound Interest = Principal * (1 + Interest Rate)^Time
In this case, the interest rate is 5.5%, so it becomes a decimal 0.055. With an initial deposit of $100 and a time of 3 years:
Compound Interest = $100 * (1 + 0.055)^3
= $100 * (1.055)^3
= $100 * 1.16603125
= $116.60 (approx.)
Therefore, the amount after three years, when interest is compounded annually, would be approximately $116.60.
To calculate the simple interest paid in the third year on an initial $100 deposit, you can use the formula:
Simple Interest = Principal × Rate × Time
In this case, the Principal is $100, the Rate is 5.5% (or 0.055), and the Time is 3 years. Plugging these values into the formula, you get:
Simple Interest = $100 × 0.055 × 3 = $16.50
Therefore, the simple interest paid in the third year on an initial $100 deposit is $16.50.
To calculate the total amount in the account after three years, you add the initial deposit to the simple interest earned.
Total Amount = Initial Deposit + Simple Interest
In this case, the Initial Deposit is $100 and the Simple Interest is $16.50. Plugging these values into the formula, you get:
Total Amount = $100 + $16.50 = $116.50
Therefore, the total amount in the account after three years is $116.50.
If the interest is compounded annually, the formula for calculating the amount after a certain number of years is:
A = P(1 + r/n)^(nt)
Where:
A = Amount after t years
P = Initial deposit
r = Interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the initial deposit is $100, the interest rate is 5.5% (or 0.055), the interest is compounded annually (so n = 1), and the time is 3 years. Plugging these values into the formula, you get:
A = $100(1 + 0.055/1)^(1×3)
Simplifying the equation, you get:
A = $100(1 + 0.055)^3
Calculating the expression inside the parentheses first:
A = $100(1.055)^3
A = $100(1.16603)
A ≈ $116.60
Therefore, if the interest is compounded annually, the amount in the account after three years is approximately $116.60.