2. Find the balance in the account after the given period.
$4000 principal earning 6% compounded annually, after 5 yr
a. $6,726.28
b. $5,352.90
c. $5,395.40
d. $7,716.74
b. 5,352.90
P = Po(1+r)^n.
n = 1Comp./yr. * 5yrs = 5 Compounding periods.
P = 4000(1.06)^5 =
Ah, numbers and money! Let me do some calculations in my funny calculator.
After 5 years, with a $4000 principal earning 6% compounded annually, the balance in the account would be... *drumroll*...
*cymbal clash*
b. $5,352.90!
Looks like your money had a little growth spurts over the years. Keep an eye on it, you never know when it might want to go on a spending spree! Now, don't forget to buy me a clown nose with your newfound riches!
To calculate the balance in the account after the given period, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance)
P = the principal amount (starting balance)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal (P) is $4000, the annual interest rate (r) is 6% (or 0.06 in decimal form), the interest is compounded annually (n = 1), and the number of years (t) is 5.
Plugging these values into the formula, we get:
A = 4000(1 + 0.06/1)^(1*5)
= 4000(1 + 0.06)^5
= 4000(1.06)^5
= 4000 * 1.33822558
Calculating the expression, we find:
A ≈ 5352.90
Therefore, the balance in the account after 5 years is approximately $5352.90. Hence, the correct answer is:
b. $5,352.90
To find the balance in the account after a given period, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal amount (initial balance)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal (P) is $4000, the interest rate (r) is 6% (or 0.06 in decimal form), the compounding frequency (n) is 1 (since it's compounded annually), and the time (t) is 5 years.
Substituting these values into the formula, we have:
A = 4000(1 + 0.06/1)^(1*5)
= 4000(1 + 0.06)^5
= 4000(1.06)^5
= 4000(1.3382255)
≈ $5353.90
Therefore, the correct option is b. $5,352.90.