Compounding frequency, time value, and effective annual rates for each of the ca
ID: 2733779 • Letter: C
Question
Compounding frequency, time value, and effective annual rates for each of the cases-----
Amount of intial deposit // Nominal annual rate// compounding frequency// deposit period
A. Calculate the future value at the ed of the specified deposit period.
B. determine the effective annual rate, EAR
C. Compare the nominal annual rate, i, to the effective annual rate, EAR. What relationship exists between compounding frequency and the nominal and effective annual rates?
A $2,400 7% 2 6 B $51,000 12% 6 4 C $1,100 6% 1 10 D $19,000 16% 3 7Explanation / Answer
C Formula for EAR =(1+r/n)^n-1 when r= npminal interest rate n= compounding frequency B A Case Initial Deposit=A Nominal Annual Rate =r Compounding frequency =n Deposit period=d Effective Annual Rate = R=(1+r/n)^n-1 Compounding factor =(1+R)^d Future Value=A*(1+R)^d A $ 2,400 7% 2 6 7.12% 1.5109 $ 3,626.06 B $ 51,000 12% 6 4 12.62% 1.6087 $ 82,041.25 C $ 1,100 6% 1 10 6.00% 1.7908 $ 1,969.93 D $ 19,000 16% 3 7 16.87% 2.9780 $ 56,581.56
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