Question

Find the annual amount of a 5 year annuity, starting at end of year 3, by converting the following cash flows to the above 5 year annuity: (a) an annuity with an annual amount of $220, starting from end of year 2 to end of year 6 plus (b) another annuity with an annual amount of $380 starting from end of year 5 to end of year 8. Use an annual interest rate 10%. (Show standard factor notation.)

Answer 1

The first annuity has 5 payments of 220 each starting at EOY 2

The second annuity has 4 payments of 380 each starting at EOY 5

i = 12%

Present value of the first annuity at EOY 0 = 220 * (P/A, 10%,5)*(P/F, 10%,1)

= 220* 3.790786* 0.90909

= 758.157

Present value of the second annuity at EOY 0 = 380*(P/A, 10%,4)*(P/F, 10%,4)

= 380* 3.16986*0.68301

= 822.723

Total present value = 758.157 + 822.723 = 1580.88

Let the third annuity be A from EOY 3 to EOY 7

Present value of the third annuity = A *(P/A, 10%,5) *(P/F,10%,2)

= A* 3.79078 * 0.826446

this should be equivalent to the present value calculated above, now

A* 3.79078 * 0.826446 = 1580.88

A = 1580.88 / (3.79078 * 0.826446)

A = 504.61