Find the amount of money in an account after 7 years if $4700 is deposited at 7% annual interest compounded quarterly.
Just use your formula.
4700(1 + .07/4)^(4*7) = ____
To find the amount of money in an account after 7 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
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 = $4700
r = 7% = 0.07 (converted to decimal)
n = 4 (compounded quarterly)
t = 7 years
Plugging in the values, we get:
A = 4700(1 + 0.07/4)^(4*7)
Now let's calculate step-by-step:
1. Calculate the interest rate per compounding period: 0.07/4 = 0.0175.
2. Calculate the exponent: 4*7 = 28.
3. Add 1 to the interest rate per compounding period: 1 + 0.0175 = 1.0175.
4. Raise the sum from step 3 to the power of the exponent from step 2: 1.0175^28.
5. Multiply the principal amount (P) by the result from step 4: $4700 * 1.0175^28.
Now let's calculate the final amount:
A = $4700 * 1.0175^28
After evaluating this expression, the amount of money in the account after 7 years should be $6,648.65 (rounded to the nearest cent).
To find the amount of money in an account after a certain period of time with compound interest, you 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 principal amount (initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case,
P = $4700
r = 7% = 0.07 (converted to decimal)
n = 4 (compounded quarterly)
t = 7 (7 years)
Substituting these values into the formula, we get:
A = 4700(1 + 0.07/4)^(4*7)
Now, let's calculate the amount of money A.