Homework SoursePresent value value of an annunity What is the presnt value
(Present value value of an annunity) What is the presnt value of the following annuities ?
a. $2,400 a year for 8 years discounted back to the presnet at 9 percent.
b. $90 a year for 5 years discounted back to the present at 8 percent.
c. 270$ a year for 12 years discounted back to the present at 12 percent.
d. 450$ a year for 6 years discounted back to the present at 5 percent
A.) What is the present value at $2,400 a year for 8 years discounted back to the present a 9 percent? $() round to nearest cent
B.)What is the present value at $90 a year for 5 years discounted back to the present at 8 perecent ? $() round to nearest cent
C.) What is the present value at $270 a year for 12 years discounted back to the present at 12 percent? () round to nearest cent
D.)What is presnt value at $450 a year for 6 years discounted back to the present at 5 perecent ? () round to nearest cent
Solution
a. Present Value of annuity $ 13,283.57 Working: 1) Present value of annuity of 1 = (1-(1+i)^-n)/i where, = (1-(1+0.09)^-8)/0.09 i 9% = 5.53481911 n 8 2) Present Value of annuity = Annual cash flow x Present Value of annuity of 1 = $ 2,400 x 5.534819 = $ 13,283.57 b. Present Value of annuity $ 359.34 Working: 1) Present value of annuity of 1 = (1-(1+i)^-n)/i where, = (1-(1+0.08)^-5)/0.08 i 8% = 3.99271 n 5 2) Present Value of annuity = Annual cash flow x Present Value of annuity of 1 = $ 90 x 3.99271 = $ 359.34 c. Present Value of annuity $ 1,672.48 Working: 1) Present value of annuity of 1 = (1-(1+i)^-n)/i where, = (1-(1+0.12)^-12)/0.12 i 12% = 6.19437 n 12 2) Present Value of annuity = Annual cash flow x Present Value of annuity of 1 = $ 270 x 6.19437 = $ 1,672.48 d. Present Value of annuity $ 2,284.06 Working: 1) Present value of annuity of 1 = (1-(1+i)^-n)/i where, = (1-(1+0.05)^-6)/0.05 i 5% = 5.07569 n 6 2) Present Value of annuity = Annual cash flow x Present Value of annuity of 1 = $ 450 x 5.07569 = $ 2,284.06
