You plan to save the following amounts 4143 today 6726 per y

You plan to save the following amounts

$4143 today

$6726 per year for the next 2 years

$6915 per year for the following 1 years

$13288 per year for the following 7 years

$17906 per year for the final 6 years

Assuming you earn a 8.1% rate of return during the entire period, how much will you have at the END of the time horizon? Round answer to the nearest dollar.

Solution

You plan to save the following amounts

$4143 today

= $4143 (F/P, 8.1%, 16)

= $4143 (1 + 0.081)^16 = 14,405 ----------------------------------------      (1)

$6726 per year for the next 2 years

= $6726 (F/P, 8.1%, 15) + $6726 (F/P, 8.1%, 14)

= $6726 (1 + 0.081)^15 + $6726 (1 + 0.081)^14 = 41, 647 ---------     (2)

$6915 per year for the following 1 years

= $6915 (F/P, 8.1%, 13)

= $6915 (1 + 0.081)^13 = 19,034 ---------------------------------------------          (3)

$13288 per year for the following 7 years

= $13288 (F/A, 8.1%, 7) (F/P, 8.1%, 6)

= $13288 [(1 + 0.081) ^ 7 – 1 ÷ 0.081] (1 + 0.081)^6

= $13288 [(1 + 0.081) ^ 7 – 1 ÷ 0.081] (1 + 0.081)^6

= $118,936 (1 + 0.081)^6 = 189,787 ------------------------------------      (4)

$17906 per year for the final 6 years

= $17906 (F/A, 8.1%, 6)

= $17906 [(1 + 0.081) ^ 6 – 1 ÷ 0.081] = 131, 686 -------------------      (5)

Total Future Value = 14,405 + 41, 647 + 19,034 + 189,787 + 131, 686

Total Future Value = 396,559