1) What is the future value of an annuity of 21 deposits of 8,700 at the end of
ID: 2772789 • Letter: 1
Question
1) What is the future value of an annuity of 21 deposits of 8,700 at the end of each year with a nominal rate of interest of 6%, compounded continuoysly, in 24 years?
A) 425383.76
B) 425585.76
C) 425583.76 (I know this answer is incorrect)
D) 425983.76
E) None of the above
2) Sara decides to set up a retirement fund by depositing $21 at the end of each day for 17 years. How much will she have then, if the interest rate is 6.25% compounded weekly and her account starts with $14,500 already deposited?
Options:
A. 274014.18
B. 274034.18
C. 274054.18
D. 274074.18
E. None of the above (This answer is incorrect)
Explanation / Answer
Ans 1.
Formula for future value of Annuity :
FV= A [ (1+k)n-1/k]
FV = Future anuuity value
A = periodical investement=$8700
K=interest rate=6% pa
n=periods=21 years
FV= 8700[{(1.06)21-1}/0.06]
=8700(3.4-1)/0.06
=348,000
After 22 years the value will be $348,000
After 24 years the value will be =348,000*1.06*1.06=$391,013
So answer is E.
2.
Formula for future value of Annuity :
FV= A [ (1+k)n-1/k]
FV = Future anuuity value
A = periodical investement=$147 per week
K=interest rate=6.25% pa=0.1198% per week
n=periods=886.42 weeks ( considering 52.14 weeks per year)
So FV= [147{1.0012}886.4-1}/0.0012
=147*1579.17
=232,137.50
Value of $14500 after 17 years = 14500(1.0012)886.4
=14500*2.895
=41,977.50
So, total value of fund=$(232,015+41,963)=$274,115.0
So the answers A to D all are near to the value derived and nearest correct is option D
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