Jim opened an account with $400. The account pays three percent quarterly. How much is in the account at the end of two years? Round to the nearest dollar. (Points : 1)
5. Use this table to answer questions 5 through 8.
Principal Rate Compounded Time Final Amount
$10,000 2% daily 5 y A
$10,000 2% quarterly 5 y B
$10,000 3% semiannually 10 y C
$10,000 3% quarterly 10 y D
Calculate A. Round to the nearest dollar.
(Points : 1)
6. Calculate B. Round to the nearest dollar. (Points : 1)
7. Calculate C. Round your answer to the nearest dollar. (Points : 1)
8. Calculate D. Round your answer to the nearest dollar. (Points : 1)
Pt = 400(1+r)^n.
r = (3%/4) / 100% = 0.0075 = Quarterly
% rate expressed as a decimal.
n = 4comp periods/yr * 2yrs = 8 Compounding periods.
Pt = 400(1.0075)^8 = $425.
5. $10,000 @ 2%, Daily, 5yrs.
Pt = Po(1+r)^n.
r = (2%/365) / 100% = 0.00005479. = Daily % rate expressed as a decimal.
n = 360 comp/yr * 5yrs = 1800 = The number of compounding periods.
Pt = 10000(1.00005479)^1800 = $11,037.
6. $10,000 @ 2%, Q, 5yrs.
r = (2%/4) / 100% = 0.005.
n = 4comp/yr * 5yrs = 20 comp. periods.
Pt = 10000(1.005)^20 = $11,049.
7. $10,000 @ 3%, Semi-ann, 10yrs.
Pt = Po(1+r)^n.
r = (3%/2) / 100% = 0.015 = Semi-annual
% rate expressed as a decimal.
n = 2comp/yr * 10yrs=20 Comp. periods.
Pt = 10000(1.015)^20 = $13,469.
8. Same procedure as 6.
To calculate the amount in the account at the end of two years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $400
r = 3% = 0.03 (since it is quarterly, divide it by 4)
n = 4 (since it is compounded quarterly)
t = 2
Now let's calculate the amount in the account at the end of two years:
A = $400(1 + 0.03/4)^(4*2)
A = $400(1 + 0.0075)^(8)
A ≈ $400(1.0075)^(8)
A ≈ $400(1.0608580625)
A ≈ $424.34
Therefore, the amount in the account at the end of two years is approximately $424.
To calculate the amount in Jim's account at the end of two years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final Amount
P = Principal (initial amount in the account)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Jim opened an account with $400, the interest rate is 3% quarterly, and the time period is 2 years.
First, let's convert the annual interest rate to a quarterly rate:
Quarterly rate = Annual rate / number of quarters in a year
Quarterly rate = 3% / 4 = 0.75%
Now, we can plug the values into the formula:
A = 400(1 + 0.0075/4)^(4*2)
A = 400(1 + 0.001875)^8
A = 400(1.001875)^8
A ≈ 400(1.0151806)
A ≈ $406.07
Therefore, at the end of two years, there will be approximately $406.07 in Jim's account.
Next, let's answer the questions using the given table:
5. Calculate A:
To calculate A, we can use the formula mentioned above. We are given the principal amount, interest rate, compounding frequency, and time period for option A.
Plugging the values into the formula:
A = $10,000(1 + 0.02/365)^(365*5)
A ≈ $11,043.33
Therefore, the amount A is approximately $11,043.33.
6. Calculate B:
We can use the same formula for option B, but with a different compounding frequency.
A = $10,000(1 + 0.02/4)^(4*5)
A ≈ $11,040.40
Therefore, the amount B is approximately $11,040.40.
7. Calculate C:
Again, using the formula, but this time with a different interest rate and time period.
A = $10,000(1 + 0.03/2)^(2*10)
A ≈ $13,439.50
Therefore, the amount C is approximately $13,439.50.
8. Calculate D:
Using the formula with the given values for option D.
A = $10,000(1 + 0.03/4)^(4*10)
A ≈ $13,822.08
Therefore, the amount D is approximately $13,822.08.
In summary:
Option A: Approximately $11,043.33
Option B: Approximately $11,040.40
Option C: Approximately $13,439.50
Option D: Approximately $13,822.08