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q1- What is the future value of 8 semi-annual payments of $331, with the first payment to occur six months from today, if the interest rate is 6% p
q1- What is the future value of 8 semi-annual payments of $331, with the first payment to occur six months from today, if the interest rate is 6% p.a.? (Don't forget to calculate the semi-annual interest rate before using the annuity formula.)
q2- What is the present value of an annuity consisting of 6 quarterly payments of $380, with the first payment to occur three months from now, if the interest rate is 12% p.a.? (Hint: You need to calculate the quarterly interest rate before you can use the annuity formula.)
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Expert Solution
1) Computation of Future Value of Annuity:
Future Value of Annuity = C*((1+i)^n - 1)/i
Here,
C = Cash Flows = $331
i = Interest Rate = 6%/2 = 3%
n = Number of Periods = 8
Future Value of Annuity = $331*((1+3%)^8 - 1)/3% = $2,943.36
2) Computation of Present Value of Annuity:
Present Value of Annuity = C*(1-(1+i)^-n)/i
Here,
C = Cash Flows = $380
i = Interest Rate = 12%/4 = 3%
n = Number of Periods = 6
Present Value of Annuity = $380*(1-(1+3%)^-6)/3% = $2,058.53
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