1. If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in
your account after 5 years?
Jawab:
PV = $10,000
I = 0.1
N =5
FVN = PV( 1 + I )N
= $10,000 ( 1 + 0.1 )5
= $16,105.1
2. What is the present value of a security that will pay $5,000 in 20 years if securities of equal
risk pay 7% annually?
Jawab:
FV = $5,000
I = 0.07
N = 20
𝐹𝑉
PV = (1+𝐼𝑁)𝑁
$5,000
= (1+0.07 )20 =
$5,000
3.87
= $𝟏, 𝟐𝟗𝟏. 𝟗𝟗
3. Your parents will retire in 18 years. They currently have $250,000 saved, and they think they
will need $1,000,000 at retirement. What annual interest rate must they earn to reach their
goal, assuming they don’t save any additional funds?
Jawab:
N = 18
PV = $250,000
FV = $1,000,000
FVN
= PV( 1 + I )N
$1,000,000 = $250,000 ( 1 + I )18
$1,000,000
$250,000
= ( 1 + I )18
4
= ( 1 + I )18
18
√4
=1+I
1.08
=1+I
I
= 1.08 – 1
= 0.08 = 8%
4.
If you deposit money today in an account that pays 6.5% annual interest, how long will it take
to double your money?
Jawab:
Diasumsikan uang saat ini = x
PV = x
FVN = 2PV = 2x
I
= 6.5%
FVN
2x
2
log(2)
= PV( 1 + I )N
= x (1 + 0.065 ) N
= (1.065) N
= N log(1.065)
N
= log(1.065) = 𝟏𝟏
log(2)
Dengan interest rate 6.5%, dibutuhkan 11 tahun agar nilai uangnya menjadi 2x dari nilai saat
ini.
5. You have $42,180.53 in a brokerage account, and you plan to deposit an additional $5,000 in
the end of every future year until your account totals $250,000. You expect to earn 12%
annually on the account. How many years will it take to reach your goal?
Jawab:
PMT = $5,000
PV = $42,180.53
∑ 𝐹𝑉 = $250,000
I
= 0.12
FVAN
=
=
FVN
(1 + 𝐼)𝑁 −1
)
𝐼
(1 + 0.12)𝑁 −1
$5,000 (
)
0.12
𝑁
(1.12) −1
$5,000 (
)
0.12
= PMT (
= PV( 1 + I )N
= $42,180.53 ( 1 + 0.12 )N
= $42,180.53 ( 1.12 )N
∑ 𝐹𝑉
= FVAN + FVN
(1.12)𝑁 −1
)
0.12
+ $42,180.53 ( 1.12 )N
$250,000
= $5,000 (
$250,000
=
$30,000
= $5,000 (1.12)𝑁 − $5,000 + $5,061.66 ( 1.12 )N
$35,000
= $5,000 (1.12)𝑁 + $5,061.66 ( 1.12 )N
$35,000
$10,061.66
= 1.12𝑁
1.12𝑁
= 3.4785
$5,000 (1.12)𝑁 −$5,000
+
0.12
$42,180.53 ( 1.12 )N
𝑁 log(1.12) = log(3.4785)
N
=
log(3.4785)
=
log(1.12)
10,99 ≈ 11
Dengan interest rate 12%, dibutuhkan 11 tahun agar nilai uangnya menjadi $250,000 dari nilai
saat ini.
6. What’s the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this was
an annuity due, what would its future value be?
Jawab:
PMT = $300
I
= 0.07
N
=5
Future Value of an Ordinary Annuity
FVAN
(1 + 𝐼)𝑁 −1
)
𝐼
5
(1 + 0.07) −1
= $300 (
)
0.07
5
(1.07) −1
= $300 (
)
0.07
0.4025
= $300 ( 0.07 ) = $𝟏, 𝟕𝟐𝟓. 𝟐𝟐
= PMT (
Future Value of an Annuity Due
FVAdue
= FVAN (1 + I)
= $1,725.22 (1 + 0.07)
= $1,845.98
7. Lin Shan is about to retire and is exploring the possibility of investing a lump sum in an annuity
so that she gets 50% of her last drawn salary at the end of every month for 15 years. She
estimates her last-drawn salary to be ¥60,000. The quotation she obtained from Ping Tan
Insurance requires her to invest a lump sum of ¥1 million. Calculate the return that Lin Shan
is earning on her annuity.
Jawab:
PMT = ¥60,000
n
= 15
i
= 0.5
Total Contribution = invest awal + PMT (N) (jumlah bulan)
= ¥1,000,000+ (¥60,000 (15)(12))
= ¥11,800,000
(1 + 𝑖)𝑛 −1
)
𝑖
(1 + 0.5)15 −1
¥60,000 (
)
0.5
= PMT (
FV
=
= ¥26,273,633.42
Return = (FV – Total Contribution)/12
= (¥26,273,633.42 - ¥11,800,000)/12
= ¥1,206,136 pertahun
8. An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4,
$300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk
earn 8% annually, what is its present value? Its future value?
Jawab:
FV = 100; 100; 100; 200; 300; 500
I = 0.08
N = 1; 2; 3; 4; 5; 6
NPV = ∑ (
𝐹𝑉𝑁
1+𝐼 )𝑁
$100
= (1+0.08 )1 +
$100
(1+0.08 )2
+
$100
(1+0.08 )3
+
$200
(1+0.08 )4
+
$300
(1+0.08 )5
+
$500
(1+0.08 )6
= 92.5926 +85.7339 +79.3832 + 147.006 +204.1749 +315.0848
= $923.9754
FVN
= PV( 1 + I )N
= $923.9754 (1+0.08)6
= $1,466.2328
9. You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized
over 5 years (60 months), and the nominal interest rate will be 12% with interest paid monthly.
What will be the monthly loan payment? What will be the loan’s EAR?
Jawab:
Monthly rate = i = 0.12 / 12 = 0.1
Yearly rate = I = 0.12
N of months = N = 60
Compound = M = 12
1
(1+𝑖)𝑁
1−
PVAN
= PMT (
𝑖
$20,000 = PMT (
1−
)
1
(1+0.1)60
0.1
)
$20,000 = PMT (9.9671)
$20,000
=
9.9671
PMT
=
$2,006.60
EAR
= [1 + ] − 1
𝑀
𝐼 𝑀
= [1 +
0.12 12
]
12
= 1.1268 – 1
= 0.1268
−1