if on the first of january a savings account has a balance of $3,200, what amount will be there in this account after three years if the bank gives 6% per year interest compounded quarterly? (assume that there are no deposits or withdraws of money during these three years.
find the amount after one year $1,000 invested at 6% per year if interest is a simple interest.
compound interest compounded quarterly.
3200.00 x (1.015)^12 = $3825.98 for quarterly compound interest.
For your second (simple interest) question, just increase the initial deposit by 6%.
To find out the amount in the savings account after three years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial balance)
r = annual interest rate (in decimal format)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $3,200 (initial balance)
r = 6% = 0.06 (annual interest rate in decimal format)
n = 4 (interest is compounded quarterly)
t = 3 (number of years)
Substituting these values into the formula, we get:
A = 3200(1 + 0.06/4)^(4*3)
We can simplify the equation:
A = 3200(1 + 0.015)^(12)
Now, we can calculate the value inside the parentheses:
A = 3200(1.015)^(12)
Using a calculator or spreadsheet, we find that (1.015)^(12) is approximately 1.19561803399.
A ≈ 3200 * 1.19561803399
A ≈ $3,825.79
Therefore, after three years, the amount in the savings account will be approximately $3,825.79.