SAVING
(Interest period = payment period)
• How much you will have on your saving account in 12 years, if you will
regularly save at the beginning of each month 100.00? The annually interest
rate is 6 % and the bank calculate the interest every month (Interest
period is one month).
S = 100 ∗ (1 + 0.06
12 ) ∗
(1+ 0.06
12 )(12∗12)
−1
0.06
12
After payment:
S = 100 ∗
(1+ 0.06
12 )(12∗12)
−1
0.06
12
(Interest period > payment period)
• How much you will have on your saving account in 12 years, if you will
regularly save at the beginning of each month 100.00? The annually interest
rate is 6 % and the bank calculate the interest once a year (Interest
period is one year).
S = 100 ∗ 12 ∗ (1 + 12+1
2∗12 ∗ 0.06) ∗ (1+0.06)12
−1
0.06
After payment:
S = 100 ∗ 12 ∗ (1 + 12−1
2∗12 ∗ 0.06) ∗ (1+0.06)12
−1
0.06
(Interest period < payment period)
• How much you will have on your saving account in 12 years, if you will
regularly save at the beginning of a year? The annually interest rate is
6 % and the bank calculate the interest monthly (Interest period is one
month).
S = 100 ∗ (1 + 0.06
12 )12
∗
(1+ 0.06
12 )(12∗12)
−1
(1+ 0.06
12 )12−1
After payment:
S = 100 ∗
(1+ 0.06
12 )(12∗12)
−1
(1+ 0.06
12 )12−1
ANNUITY INCOME
(Intrest period = payment period)
1
• How much do you need to put on your bank account if you like to provide
a regularly income at the end of every month in the amount of 500.00 for
17 years? The bank assures you an interest rate of 5 % p. a. (annually
interest rate) and the bank calculate the interest every month (Interest
period is one month).
R = 500 ∗
1−( 1
1+ 0.05
12
)(12∗17)
0.05
12
Ahead payment:
R = 500 ∗
1−( 1
1+ 0.05
12
)(12∗17)
1− 1
1+ 0.05
12
(Intrest period > payment period)
• How much do you need to put on your bank account if you like to provide
a regularly income at the end of every month in the amount of 500.00 for
17 years? The bank assures you an interest rate of 5 % p. a. (annually
interest rate) and the bank calculates the interest once a year (Interest
period is one year).
R = 500 ∗ 12 ∗ (1 + 12+1
2∗12 ∗ 0.05) ∗
1−( 1
1+0.05 )17
0.05
Ahead payment:
R = 500 ∗ 12 ∗ (1 + 12−1
2∗12 ∗ 0.05) ∗
1−( 1
1+0.05 )17
0.05
(Intrest period < payment period)
• How much do you need to put on your bank account if you like to provide
a regularly income at the end of a year (Payment period is one year, just
once a year you will obtain 500.00) in the amount of 500.00 for 17 years?
The bank assures you an interest rate of 5 % p. a. (annually interest rate)
and the bank calculates the interest every month (Interest period is one
month).
R = 500 ∗ ( 1
1+ 0.05
12
)12
∗
1−( 1
1+ 0.05
12
)(12∗17)
1−( 1
1+ 0.05
12
)12
Ahead payment:
R = 500 ∗
1−( 1
1+ 0.05
12
)(12∗17)
1−( 1
1+ 0.05
12
)12
2