Comparing compounding periods Personal Finance Problem René Levin wishes to dete

Question

Comparing compounding periods Personal Finance Problem René Levin wishes to determine the future value at the end of 8 years of a $18,500 deposit made today into an account paying a nominal annual rate of 12% a. Find the future value of René's deposit, assuming that interest is compounded (1) annually. (2) quarterly, (3) monthly, and (4) continously b. Compare your findings in part a, and use them to demonstrate the relationship between compounding frequency and future value. c. What is the maximum future value obtainable given the $18.500 deposit the 8-year time period and the 12 % nominal annual rate? Use your findings n at ato explain. a.(1) For annual compounding. the future value of René's deposit is Round to the nearest cent.) 2) For quarterly compounding the future value of René's deposit is s(Round to the nearest cent) (3) For monthly compounding, the future value of René's deposit is s(Round to the nearest cent) 4) For continous compounding, the future value of René's deposit is (Round to the nearest cent b.Compare your findings in part a, and use them to demonstrate the relationship between compounding frequency and future value. (Select the best answer below.) O A. The more frequently interest is compunded, the lower the future value will be O B. The more frequently interest is compunded, the higher the future value will be ° C. The frequency of the compounding does not affect the future value. O D. The less frequently interest is compunded, the higher the future value will be c. The maximum future value obtainable given the S 18,500 deposit, the 8-year time period, and the 12% nominal annual rate is S Round to the nearest cent

Explanation / Answer

a
Future value=Present value*(1+r/m)^(m*t)
where m is compounding periods per year and t is number of years
1
=18500*(1+12%/1)^(8*1)
=45805.32
2
=18500*(1+12%/4)^(8*4)
=47639.03
3
=18500*(1+12%/12)^(8*12)
=48086.54912
4
=18500*e^(12%*8)
=48316.38

b
Option B
The more frequently interest is compounded, the higher the future value will be

c
Maximum occurs at continous compounding
Value=$48316.38

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