You put $5,000 in an account that is compounded quarterly. The annual interest rate, r, is 4%. How much will be in the account after 10 years?
A.$5,523.11
B.$5,747.37
C.$7,444.32
D.$24,005.10
I've tried this so many times and I have no idea please help!
P = Po(1+R)^n,
R = 0.04/4 = 0.01 = quarterly % rate expressed as a decimal.
n = 10yrs * 4comp./yr. = 40 compounding periods.
P = 5000(1+0.01)^40 = $7444.32.
quarterly means four compounding periods per year
... each at a quarter of the full interest rate
a = 5000 [1 + (.04 / 4)]^(10 * 4)
To calculate the amount in the account after 10 years with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account after time t
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, P = $5,000, r = 0.04 (because the annual interest rate is 4%), n = 4 (since interest is compounded quarterly), and t = 10.
Substituting these values into the formula:
A = $5,000(1 + 0.04/4)^(4*10)
Calculating the values within the parentheses first:
A = $5,000(1 + 0.01)^(40)
Simplifying within the parentheses:
A = $5,000(1.01)^(40)
Using a calculator, evaluate the expression within the parentheses, and then multiply by $5,000:
A ≈ $5,000(1.488641)
A ≈ $7,443.21
Therefore, the correct answer is C. $7,444.32.
To find the amount of money in the account after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount of money in the account
P = the original principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the original principal amount (P) is $5,000, the annual interest rate (r) is 4% (or 0.04 as a decimal), the interest is compounded quarterly (n = 4), and we want to find the amount after 10 years (t = 10).
Plugging in these values into the formula:
A = $5,000(1 + 0.04/4)^(4*10)
Simplifying the expression inside parentheses:
A = $5,000(1 + 0.01)^(4*10)
A = $5,000(1.01)^40
Now we can calculate the final amount. Using a calculator:
A ≈ $5,000(1.488886502)
A ≈ $7,444.33
Therefore, the amount in the account after 10 years would be approximately $7,444.33.
So the correct answer is C. $7,444.32.