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?

To calculate the amount in the account after 10 years with quarterly compounding interest, you can use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the account
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

In this case, you have:
P = $5,000 (principal amount)
r = 4% = 0.04 (annual interest rate as a decimal)
n = 4 (since interest is compounded quarterly)
t = 10 years

Now, let's substitute these values into the formula and calculate the future value, A:

A = $5,000 * (1 + 0.04/4)^(4 * 10)

First, simplify the term inside the parentheses:
A = $5,000 * (1 + 0.01)^(40)

Next, calculate the exponent:
A = $5,000 * (1.01)^(40)

Finally, evaluate the expression:
A ≈ $5,000 * 1.488344

A ≈ $7,441.72

Therefore, after 10 years, there will be approximately $7,441.72 in the account.

To solve this problem, we will use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/amount in the account after t years
P = the initial principal/amount invested
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

Given:
P = $5,000
r = 4% = 0.04 (as a decimal)
n = 4 (compounded quarterly)
t = 10 years

Using the given values, we can now calculate the amount in the account after 10 years.

A = 5000(1 + 0.04/4)^(4*10)
A = 5000(1 + 0.01)^(40)
A = 5000(1.01)^(40)
A ≈ $7,321.94

Therefore, after 10 years, there will be approximately $7,321.94 in the account.

4% means 1% per quarter (compounding period)

10 yr is 40 quarters

A = 5000 (1 + .01)^40