Compound Amount Factors Course 4

Gradient Formula Gradient formula terdiri atas dua tipe yakni uniform gradient dan geometric gradient. Gradien seragam merupakan seri cash flow yang mempunyai peningkatan dan penurunan yang seragam (uniformly increasing/decreasing). Gradien geometrik merupakan seri cash flow yang mempunyai tingkat perbandingan penurunan/peningkatan yang seragam (uniform rate). Besar penurunan atau peningkatan adalah gradien. Payment that occurs at the end of year 1 is not a part of the gradient series but is rather a base payment.

Uniform Gradient Guna : menentukan A, diketahui G Simbol : (A/G, i%, n) Rumus : A = G 1 – n i (1+i)n – 1 = G (A/G, i%, n)

Diagram Cash Flow A = ? G = Diket 1 2 3 4 5 6 7 n-1 n

Penurunan Rumus : P = ? G = Diket 2G G P = Diket A = ? 2G G (n-1)G 1 2 3 n-1 n P = Diket A = ? G 2G (n-2)G (n-1)G 1 n 2 3 n-1

Contoh Soal 7 G = 10 A = ? 10 20 30 40 1 2 3 4 5

Contoh Soal 8 A = ? 10 15 20 25 1 2 3 4 5

25 20 15 A2=? 10 A1=10 1 2 3 4 5 Atot = A1 + A2

Increase - Decrease = atau ≠ A1 = ? 10 30 20 40 G = 10 A2 = ? 10 30 20 3 4 5 10 30 20 40 G = 10 = atau ≠ A2 = ? 1 2 3 4 5 10 30 20 40 G = 10

Decrease -

Contoh Soal 9 40 30 20 10 1 2 3 4 5

Guna : menentukan P, diketahui G PE = D ( n ) ; E=i Geometric Gradient Guna : menentukan P, diketahui G PE = D ( n ) ; E=i PE = D [ (1+E)n/(1+i)n – 1] ; E≠i 1 + E 1 - E

Diagram Cash Flow PE 1 4 n D D(1+E) D(1+E)2 D(1+E)3 D(1+E)n-1

Contoh Soal A new pickup truck has a first cost of $8000 and is expected to last 6 years with a $1300 salvage value. The operating cost of vehicle is expected to be $1700 the first year incresing by 11% per year after. Determine the equivalent cost of truck if the interest rate id 8% per year.

Solusi P = 8000 + PE – 1300 (P/F,8%,6) = 8000 + 1700 [ (1+0,11)/(1+0,08)]6 – 1 - 1300 (P/F,8%,6) 0,11 – 0,08 = $17305, 85

Homework Perusahaan Free Spirit Liquor mematok pendapat sebesar $47.000 pada tahun depan dari penjualan produknya. Penjualan diharapkan meningkat secara seragam sehingga mencapai $100.000 dalam 8 tahun. Tentukan gradien dan diagram cash flow-nya. The first year maintenance cost for a new automobile is estimated to be $100 and it increases at a uniform rate of 10% per year.what is the present worth of cost of the first five years of maintenance in this situation, using an 8% interest rate.