if on the first of january a savings acctount has a balance of 3,200. what amount will be in this account after 3 years if the bank gives 6% per year interest compounded quarterly?
$3,825.98
not much huh?
3 years = 12 periods
.06 per year = .015 per period
so
3200 * 1.015^12 = 3825.98 indeed
To calculate the amount in the savings account after 3 years with 6% interest compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount in the account
P = the initial balance (3,200)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (quarterly, so 4)
t = the number of years (3)
Now, let's substitute these values into the formula and calculate the future amount:
A = 3200(1 + 0.06/4)^(4*3)
A = 3200(1 + 0.015)^(12)
A = 3200(1.015)^(12)
A ≈ 3200(1.195618)
A ≈ 3834.99
Therefore, after 3 years, the amount in the savings account will be approximately $3,834.99.