can someone correct these for me thanks..
Problem #4
Find the effective rate corresponding to the given nominal 18% compounded quarterly.
My answer: 19.2%
Problem #7
Find the future value of the ordinary annuity If R= $2500,I=5% interest compounded quarterly for 16 years.
My answer: Future value $59,143.72
Problem#10
Find the present value of the ordinary annuity payments of $17000 annually for 10 years at 12% compounded annually.
my answer $1,184,908.87
10. Obviously wrong. 17,000 x 10 years is 170, 000 and the present value cannot be more than that.
7. No, I get considerably less than that.
You can check these yourself at
http://www.uic.edu/classes/actg/actg500/pfvatutor.htm
To find the effective rate corresponding to a given nominal rate compounded quarterly (Problem #4), you can use the formula:
Effective rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1
Substituting the values given, we get:
Effective rate = (1 + (18% / 4))^4 - 1
= (1 + 0.045)^4 - 1
= (1.045)^4 - 1
= 1.193925 - 1
= 0.193925 or 19.3925%
So, the correct effective rate is 19.3925%, not 19.2%.
To find the future value of an ordinary annuity (Problem #7), you can use the formula:
Future Value = R * [(1 + (I / number of compounding periods))^(number of compounding periods * number of years) - 1] / (I / number of compounding periods)
Substituting the values given, we get:
Future Value = $2500 * [(1 + (5% / 4))^(4 * 16) -1] / (5% / 4)
= $2500 * [(1 + 0.0125)^(64) -1] / (0.05 / 4)
≈ $2500 * (1.0125^64 - 1) / 0.0125
≈ $59,392.28 (rounded to the nearest cent)
Therefore, the correct future value of the ordinary annuity is $59,392.28, not $59,143.72.
For Problem #10, the given answer is incorrect. It states that the present value of an ordinary annuity is $1,184,908.87 for annual payments of $17,000 over 10 years at a 12% interest rate compounded annually.
However, this answer is clearly incorrect since the total amount of payments over 10 years is only $170,000 (17,000 * 10). The present value is a measure of the current value of future cash flows, and it cannot exceed the total amount of cash flows.
You may use a present value annuity formula to calculate the correct answer. The formula is:
Present Value = R * [(1 - (1 + I)^(-n)) / I]
Substituting the values given, we get:
Present Value = $17,000 * [(1 - (1 + 12%)^(-10)) / 12%]
= $17000 * [(1 - (1.12)^(-10)) / 0.12]
≈ $103,417.13 (rounded to the nearest cent)
Therefore, the correct present value of the ordinary annuity payments is approximately $103,417.13, not $1,184,908.87.