Juanita Finn deposits $12,000 into an account at Valley Bank that pays 8% interest compounded quarterly. At the end of 5 years, how much will Juanita have in her account? Round to the nearest cent.
To calculate the amount Juanita will have in her account at the end of 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case:
P = $12,000
r = 8% = 0.08
n = 4 (since interest is compounded quarterly)
t = 5 years
Substituting the values into the formula:
A = $12,000(1 + 0.08/4)^(4*5)
Let's calculate the result step by step:
A = $12,000(1 + 0.02)^(20)
A = $12,000(1.02)^(20)
Now we can use a calculator or follow the step-by-step calculation:
A ≈ $12,000 * 1.485947
A ≈ $17,831.36
Therefore, at the end of 5 years, Juanita will have approximately $17,831.36 in her account.
To calculate the amount Juanita will have in her account at the end of 5 years, 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 = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Now let's break down the information provided:
P = $12,000
r = 8% = 0.08 (expressed as a decimal)
n = 4 (compounded quarterly)
t = 5 years
Plugging these values into the formula, we have:
A = 12000(1 + 0.08/4)^(4*5)
First, we divide the annual interest rate (0.08) by the number of times it is compounded per year (4) to get the quarterly interest rate (0.02). Then we raise this quarterly rate to the power of the total number of compounding periods (4*5 = 20).
A = 12000(1.02)^20
Calculating the exponent:
A = 12000 * 1.4859464
A ≈ $17,831.36
Therefore, Juanita will have approximately $17,831.36 in her account at the end of 5 years.
i = .08/4 = .02 ----- because of "compounded quarterly"
n = 5(4) = 20 ----- there are 20 quarters.
plug into "amount of annuity" formula