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Resource: Ch. 5 of the text
Calculate the future value of the following:
o $5,000 compounded annually at 6% for 5 years
o $5,000 compounded semiannually at 6% for 5 years
o $5,000 compounded quarterly at 6% for 5 years
o $5,000 compounded annually at 6% for 6 years
(a) i = 6% = 0.06 and n = 5
FV = 5000 * [(1 + 0.06)^5 - 1] / 0.06 = $28185.46
(b) i = 3% = 0.03 and n = 10
FV = 5000 * [(1 + 0.03)^10 - 1] / 0.03 = $57319.40
(c) i = 1.5% = 0.015 and n = 20
FV = 5000 * [(1 + 0.015)^20 - 1] / 0.015 = $115618.34
(d) i = 6% = 0.06 and n = 6
FV = 5000 * [(1 + 0.06)^6 - 1] / 0.06 = $34876.59
Answer the following: What conclusions can be drawn about the frequency of compounding interest? What conclusions can be drawn about the length of time an amount is compounding?
As the frequency of compounding interest increases, the future value of the annuity also increases.As the length of time an amount is compounding increases, the future value of the annuity also increases.
Calculate the present value of the following:
o $7,000 in 5 years at an annual discount rate of 6%
o $7,000 in 5 years at a semiannual discount rate of 6%
o $7,000 in 5 years at a quarterly discount rate of 6%
o $7,000 in 6 years at an annual discount rate of 6%
(a) i = 6% = 0.06 and n = 5
PV = 7000 * [1 - (1 + 0.06)^-5] / 0.06 = $29486.55
(b) i = 3% = 0.03 and n = 10
PV = 7000 * [1 - (1 + 0.03)^-10] / 0.03 = $59711.42
(c) i = 1.5% = 0.015 and n = 20
PV = 7000 * [1 - (1 + 0.015)^-20] / 0.015 = $120180.47
(d) i = 6% = 0.06 and n = 5
PV = 7000 * [1 - (1 + 0.06)^-6] / 0.06 = $34421.27
Answer the following: What conclusions can be drawn about the frequency of the discounting interval? What conclusions can be drawn about the length of time until the receipt of that value?
As the frequency of compounding interest increases, the present value of the annuity also increases.As the length of time an amount is compounding increases, the present value of the annuity also increases.
Answer the following: Assume you have a choice between two annuity contracts. Contract A pays $5,000 per year for 5 years starting one year from today. Contract B pays $5,000 per year for 5 years starting today. The discount rate for each is 6%. Which annuity contract would you choose for your retirement? Why?
Contract A (Ordinary Annuity):PV = PMT * [1 - (1 + i)^-n] / i
PV = 5000 * [1 - (1 + 0.06)^-5] / 0.06 = $21061.82
Contract B (Ordinary Due):
PV = PV of ordinary annuity * (1 + i) = 21061.82 * (1 + 0.06) = $22325.53
Since Contract B has a higher PV, we choose Contract B.