Question

B-7. Calculate the future value of $4,000 per year investment (ordinary annuity) ten years from now if the annual rate of return is: (2 pts each) a. 4% b. 6%c. 10% B-7a. Explain why are results for C is greater than B is greater than A B-8. Calculate the future value of $4,000 per year investment (ordinary annuity) twenty years from now if the annual rate of return is: a. 4% b. 6%c. 10% B-9. Explain why are all of the results for B8 are greater than their corresponding letter results for B7 even though the rate of returns are the same. (4pts) B.10 Find the present value of a ten-year ordinary annuity of $5,000, using the following discount rates: (2 pts each) a. 5% b. 8% c. 12% B-10a. Explain why are results for C is less than B is less than A

Answer 1

B-7  

future value of $4,000 per year investment (ordinary annuity) ten years from now

a) when the annual rate of return is 4%

= 4000/0.04*(1.04^10-1)

=$48024.43

b) when the annual rate of return is 6%

= 4000/0.06*(1.06^10-1)

=$52723.18

c) when the annual rate of return is 10%

= 4000/0.1*(1.1^10-1)

=$63749.70

B-7a)

The results for c) is greater than b) and b) is greater than a) because the Interest rate is higher for c) than for b) and higher for b) than for a) . Because of this, Accumulated amounts increase fastest for c) followed by b) and then for a)

B-8

future value of $4,000 per year investment (ordinary annuity) twenty years from now

a) when the annual rate of return is 4%

= 4000/0.04*(1.04^20-1)

=$119112.31

b) when the annual rate of return is 6%

= 4000/0.06*(1.06^20-1)

=$147142.36

c) when the annual rate of return is 10%

= 4000/0.1*(1.1^20-1)

=$229100.00

B-9)  all of the results for B8 are greater than their corresponding letter results for B7 even though the rate of returns are the same. This happens becuase of the time difference . All the investments in B7 were for 10 years and in B8 for 20 years. Thus, the amounts get more time to be compounded and hence the Future value of annuities in B8 are higher.

B10)

present value of a ten-year ordinary annuity of $5,000

a) when the discount rate is 5%

= 5000/0.05*(1-1/1.05^10)

=$38608.67

b)when the discount rate is 8%

= 5000/0.08*(1-1/1.08^10)

=$33550.41

c) when the discount rate is 5%

= 5000/0.12*(1-1/1.12^10)

=$28251.12

B10 a)

The results for c) is less than b) is less than a) because of interest rates. the Present value of an amount with higher interest rates is lesser and similarly the present value of an annuity with higher interest rates is lesser.