Find the balance in the account after the given period.
$500 principal earning 4% compounded quarterly, after 6 yr
a. $1,281.65
b. $634.87
c. $709.26
d. $632.66
conert 4% to decimal= .04
quarterly= 4 so the problem would go
a=p(1+r/n)^nt
a=500(1+.04/4)^4x6
500(1.01)^24
500(1.26973)
634.865 but round to 634.87 :)
answer: 634.87
$634.87.
P = Po(1+r)^n.
Po = $500, r = (4%/4)/100% = 0.01
= Quarterly % rate expressed as a deci8mal.
n = 4Comp./yr. * 6yrs = 24 Compounding periods.
P = ?.
$634.87
To find the balance in the account after the given period, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final balance
P = the principal amount (initial investment)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal is $500, the interest rate is 4% (or 0.04 as a decimal), and the interest is compounded quarterly (n = 4). The time period is 6 years.
Using the formula, we can calculate the balance:
A = 500(1 + 0.04/4)^(4*6)
= 500(1 + 0.01)^(24)
= 500(1.01)^(24)
= 500(1.268241)
≈ $634.87
Therefore, the balance in the account after 6 years is approximately $634.87.
The correct answer is option b.
Well, let me take out my calculator and clown nose for this one!
To find the balance after 6 years with quarterly compounding, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value
P is the principal amount ($500 in this case)
r is the annual interest rate (4% = 0.04)
n is the number of times interest is compounded per year (quarterly = 4)
t is the number of years (6)
Plugging in the values, we get:
A = 500(1 + 0.04/4)^(4*6)
= 500(1 + 0.01)^(24)
= 500(1.01)^(24)
≈ 632.66
So the answer is option d. $632.66.