Sharp CS-2870 CS-2870 Operation Manual - Page 25

Annual, Quarterly, Principal, balance

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COMPOUND INTEREST Calculate the new balance on a deposit which is compounded quarterly for 4 years at a given annual interest rate. SOLUTION: 1. Calculate the quarterly interest rate. 2. Calculate the new balance (principal plus interest) FORMULA: New balance = P (1 + Where P = amount of deposit (principal) = interest rate per period n = number of years x 4 EXAMPLE: If P = $6,150 i = 5% annum ÷ 4 periods = 0.0125 n = 4 years x 4 periods = 16 Then 6,150 (1 + 0.0125)76 $7,502.32 (New Balance) (1) (2) (3) (4) ffif -F -6 -5 -4 -3 -2 -1 -o .05 4 1 0.05 0.0125 0.0125 1.0125 0.05 4. = 0.0125 * 0.0125 + 1• + 1.0125 0 Annual int. rate Quarterly int. rate (1 +i) 1.0125 O 1.02515625 O 1.02515625 1.05094533691 1.0125 x 1.0125 = 1.02515625 * 1.02515625 x 1.02515625 = 1.05094533691 * (1 + i)2 (1 + i)4 1.05094533691 E1 1.10448610117 1.05094533691 x 1.05094533691 = 1.10448610117 * (1 + 1)8 1.10448610117 1.21988954767 1.10448610117 x 1.10448610117 = 1.21988954767 * (1 + 016 6150 El 1.21988954767 7,502.32071817 1.21988954767 x 6150• = 7,502.32071817 *- Principal New balance 23

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COMPOUND
INTEREST
Calculate
the
new
balance
on
a
deposit
which
is
compounded
quarterly
for
4
years
at
a
given
annual
interest
rate.
SOLUTION:
1.
Calculate
the
quarterly
interest
rate.
2.
Calculate
the
new
balance
(principal
plus
interest)
FORMULA:
New
balance
=
P
(1
+
amount
of
deposit
(principal)
interest
rate
per
period
number
of
years
x
4
$6,150
5%
annum
÷
4
periods
=
0.0125
4
years
x
4
periods
=
16
Where
P
=
n
=
=
EXAMPLE:
If
P
i
n
=
=
=
Then
(1)
6,150
(1
(2)
+
0.0125)
76
$7,502.32
(
3
)
(New
Balance)
(4)
ffif
-F
.05
0.05
0.05
Annual
int.
rate
-6
-5
4
4.
=
-4
-3
0.0125
0.0125
*
Quarterly
int.
rate
-2
-1
0.0125
0.0125
+
-o
1
1.0125
1•
+
1.0125
0
(1
+i)
1.0125
1.0125
x
O
1.0125
=
1.02515625
1.02515625
*
(1
+
i)
2
O
1.02515625
1.02515625
x
1.02515625
=
1.05094533691
1.05094533691
*
(1
+
i)
4
1.05094533691
1.05094533691
x
E1
1.05094533691
=
1.10448610117
1.10448610117
*
(1
+
1)8
1.10448610117
1.10448610117
x
1.10448610117
=
1.21988954767
1.21988954767
*
(1
+
0
16
1.21988954767
1.21988954767
x
6150
El
6150•
=
Principal
7,502.32071817
7
,
502.32071817
*-
New
balance
23