Question

4. (a) What is the future value of a 3-year ordinary annuity (recall that ordinary annuities have end of year cash flows) of $200 if the appropriate interest rate is 12%? (1 point) (b) What is the present value of the annuity? (1 point) (c) What would the future and present values be if the annuity were an annuity due (beginning of year cash flows)? Hint, set your calculator to BGN, there is a video in M2 that shows you how to do this. Don't forget to reset to "END" after you work an annuity due problem (1 pt) PV = (1 pt) FV =

Answer 1

(a)

The future value of the annuity is calculated below:

Future value = 200 x ((1+0.12)3 - 1 0.12

Future value = 200 x 3.3744

Future value = 674.88

(b)

The present value of the same annuity is calculated below:

Present value = 200 x 1- (1 + 0.12)-3 0.12

Present value = 200 x 2.40183

Present value = 480.37

(c)

The future value of the annuity is calculated below:

Future value = 200 x (1 +0.12) - 1 1 - 1.12-1

Future value = 200 x 3,3779328

Future value = 755.87

The present value of the same annuity is calculated below:

Present value = 200 x 1- (1 + 0.12)-3 1-1.12-1

Present value = 200 x 2.69

Present value = 538.01