Changing compounding frequency Using annual, semiannual, and quarterly compoundi
ID: 2806006 • Letter: C
Question
Changing compounding frequency Using annual, semiannual, and quarterly compounding periods, (1) calculate the future value if $5,000 is deposited initially, and (2) determine the effective annual rate (EAR). a. At 12% annual interest for 5 years. b. At 16% annual interest for 6 years. C. At 20% annual interest for 10 years. a. Annual Compounding (1) The future value, FWs SD (Round to the nearest cent) (2) If the 12% annual nominal rate is compounded annually, the EAR is (Round to two decimal places.) (1) The future value, FVn is s(Round to the nearest cent) (2) If the 12% annual nominal rate is compounded semiannually, the EAR is | |%. (Round to two decimal places.) (1) The future value, FV., is $. (Round to the nearest cent) (2) If the 12% annual nominal rate is compounded quarterly, the EAR is b. Annual Compounding (1) The future value, FVn, is (Round to the nearest cent) (2) If the 16% annual nominal rate is compounded annually, the EAR is 96 (Round to two decimal places.) 1%. (Round to two decimal places.)Explanation / Answer
A. Annual compounding @12% for 5 years = 5000*(1.12)^5= 8811.71$
12% annual compounding EAR= (1.12)^1 - 1= 12%
2. Semiannual compounding 12% for 5 years
FV= 5000*(1.06)^10= 5000*1.79084= 8954.24$
EAR={ (1.06)^2 - 1}*100= 12.36%
3. Quarterly compounding 12% for 5 years
FV= 5000*(1.03)^20= 5000*1.8061= 9030.55$
EAR= (1.03)^4-1
= 12.55%
B. 1. Annual compounding for 16% for 6 years
FV= 5000*(1.16)^6= 5000*2.436= 12181.98$
EAR= 16%
Semiannual compounding 16% for 6 years
FV= 5000*(1.08)^12= 2.5181*5000= 12590.85$
EAR= (1.08)^2-1= 16.64%
Quarterly compounding 16% for 6 years
FV= 5000*(1.04)^24= 5000*2.563= 12816.52$
EAR= (1.04)^4-1= 16.98%
3. Annual compounding for 20% 10 years
FV= 5000*(1.20)^10= 5000*6.192= 30958.68$
Ear= 20%
Semiannual compounding 20% for 10 years
FV= 5000*(1.10)^20= 33637.49$
EAR= (1.1)^2-1= 21%
Quarterly compounding for 20% for 10 years
FV= 5000*(1.05)^40= 35199.9 4$
EAR= (1.05)^4-1= 21.55%
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