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Calculating present and future values

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13. The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ______.
A. $253.00
B. $252.00
C. $158.00
D. $134.66

14. The future value of $100 received today and deposited at 6 percent for four years is
A. $126.
B. $ 79.
C. $124.
D. $116.

15-19. Calculate the present value of the annuity assuming that it is an ordinary annuity.

Case Amount of Annuity Interest Rate Period / Years
A $14,000 9% 3
B $17,500 13% 15
C $975 18% 7
D $1,127,000 4% 9
E $10,000 7% 3

20-24. For each of the cases shown below in the table, calculate the present value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years
A $13,000 10% 5
B $34,000 17% 25
C $16,000 6% 18
D $210,000 15% 15
E $90,000 20% 9

25-29 For each of the cases shown below in the table, calculate the future value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years
A $3,000 10% 7
B $44,000 12% 5
C $6,000 8% 10
D $27,000 16% 12
E $99,000 20% 6

Calculate the above future values in questions 25-29 as semi annual and quarterly compounding.

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Solution Summary

There are basic 17 problems related to time value of money concepts. Solutions depict the methodology to calculate Present and future values in different cases.

Solution Preview

Please refer attached file for better clarity of formulas.

Present Value of deposit=PV=$200
Semi annual interest rate=i=8%/2=4%
Number of periods=n=3 years=6 (semi annual periods)
Future Value of deposit=PV*(1+i)^n=200*(1+4%)^6=253.06

Answer is A. $253


Present Value of deposit=PV=$100
Annual interest rate=i=6%
Number of periods=n=4 years
Future Value of deposit=PV*(1+i)^n=100*(1+6%)^4=126.2477

Answer is A. $126


Case A:
Amount of annuity=R=$14000
Interest rate=i=9%
Periods=n=3 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=14000*(1-1/(1+9%)^3)/9%=$35,438.13

Case B:
Amount of annuity=R=$17500
Interest rate=i=13%
Periods=n=15 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=17500*(1-1/(1+13%)^15)/13%=$113,091.63

Case C:
Amount of annuity=R=$975
Interest rate=i=18%
Periods=n=7 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=975*(1-1/(1+18%)^7)/18%=$3,716.24

Case D:
Amount of annuity=R=$1,127,000
Interest rate=i=4%
Periods=n=9 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=1127000*(1-1/(1+4%)^9)/4%=$8,379,618.7

Case ...

Solution provided by:
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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