Matakuliah
Tahun
: Manajemen Keuangan 1
: 2009
NILAI WAKTU DARI UANG
(Time Value of Money)
Pertemuan 11
The Time Value of Money
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The Time Value of Money
Compounding and
Discounting
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If we can measure this opportunity cost,
we can:
• Translate $1 today into its equivalent in the future
(compounding).
Today
Future
?
• Translate $1 in the future into its equivalent today
(discounting).
Today
Future
?
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Future Value
(Nilai Masa Depan)
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Future Value - single sums
If you deposit $100 in an account earning 6%, how
much would you have in the account after 1 year?
PV = -100
FV = 106
0
1
Calculator Solution:
P/Y = 1
I=6
N=1
PV = -100
FV = $106
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Future Value
If you deposit $100 in an account earning 6%, how
much would you have in the account after 1 year?
PV = -100
FV = 106
0
1
Mathematical Solution:
FV = PV (FVIF i, n )
FV = 100 (FVIF .06, 1 ) (use FVIF table, or)
FV = PV (1 + i)n
FV = 100 (1.06)1 = $106
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Future Value
If you deposit $100 in an account earning 6%, how
much would you have in the account after 5 years?
PV = -100
FV = 133.82
0
5
Mathematical Solution:
FV = PV (FVIF i, n )
FV = 100 (FVIF .06, 5 ) (use FVIF table, or)
FV = PV (1 + i)n
FV = 100 (1.06)5 = $133.82
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Future Value
If you deposit $100 in an account earning 6% with
quarterly compounding, how much would you have
in the account after 5 years?
PV = -100
FV = 134.68
0
20
Mathematical Solution:
FV = PV (FVIF i, n )
FV = 100 (FVIF .015, 20 ) (can’t use FVIF table)
FV = PV (1 + i/m) m x n
FV = 100 (1.015)20 = $134.68
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Present Value
(Nilai Sekarang)
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Menentukan Suku Bunga
If you sold land for $11,933 that you bought 5 years
ago for $5,000, what is your annual rate of return?
Mathematical Solution:
PV = FV (PVIF i, n )
5,000 = 11,933 (PVIF ?, 5 )
PV = FV / (1 + i)n
5,000 = 11,933 / (1+ i)5
.419 = ((1/ (1+i)5) ..... Lihat tabel PVIF
Maka, ditemukan i = 19% (i=19%, n=5)
PVIF = 0.419
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Contoh lain, sebuah bank menawarkan pinjaman Rp 25.000 kepada anda
untuk membeli sebuah perlengkapan rumah.Untuk itu anda harus
menanda tangani perjanjian yang berisi persyaratan bahwa anda harus
mengangsur Rp 2.545,16 setiap akhir tahun selama 25 tahun. Berapa
besarnya suku bunga yang dibebankan bank tersebut?

Diketahui PV = RP 25.000 dari nilai sekarang anuitas RP
2.545,16 selama 25 tahun :
PV = RP 25.000 =  2.545,16 [ 1 : (1 + i)n] = 2.545,16 (PVIFAi, 25
tahun ).

Cari nilai PVIFAi, 25 tahun :
= 25.000 : 2.545,16
= 9,8226

Lihat tabel PVIFA pada kolom periode 25 cari angka 9,8226
dan yang paling mendekati angka tersebut adalah 9%. Jadi
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suku bunga dari kredit hipotik tersebut adalah 9% setahun. 18
Menentukan Periode (N)
Suppose you placed $100 in an account that pays
9.6% interest, compounded monthly. How long will
it take for your account to grow to $500?
Mathematical Solution:
PV = FV / (1 + i)n
100 = 500 / (1+ .008)N
5 = (1.008)N
ln 5 = ln (1.008)N
ln 5 = N ln (1.008)
1.60944 = .007968 N
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N = 202 months
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