Question

If you invest $17,500 today, how much will you have in each of the following instances? Use Appendix A as an approximate answer, but calculate your final answer using the formula and financial calculator methods.

a. In 7 years at 8 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

b. In 18 years at 7 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

c. In 25 years at 6 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

d. In 20 years at 6 percent (compounded semiannually)? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

How much would you have to invest today to receive the following? Use Appendix B or Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

  
e. $14,600 in 7 years at 13 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

f. $18,800 in 18 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

g. $7,600 each year for 16 years at 14 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

h. $51,000 each year for 50 years at 8 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

Answer 1

For parts a to d we need to calculate future value and for parts e to h we need to calculate the present value.

Future value (FV) = Amount x (1 + r)ⁿ

Present value (PV) = Amount / (1 + r)ⁿ

where, r = interest rate, n = no. of years

a) FV = $17500 x (1 + 0.08)⁷ = $29,991.92

b) FV = $17500 x (1 + 0.07)¹⁸ = $59,148.81

c) FV = $17500 x (1 + 0.06)²⁵ = $75,107.74

d) Since it is compounded semi-annually, we require semi-annual interest rate and time periods -

No. of semi-annual periods (n) = 20 x 2 = 40

semi-annual Interest rate (r) = 6% / 2 = 3%

FV = $17500 x (1 + 0.03)⁴⁰ = $57,085.66

e) PV = $14600 / (1 + 0.13)⁷ = $6,205.89

f) PV = $18800 / (1 + 0.11)¹⁸ = $2,873.06

g) $7600 is to be received each year. This is a form of annuity. Present value of an annuity is computed as -

h) Same as g.