Assignment 4 Muhammad Arif Naufal
18522032
1. A man deposit $500 in a credit union at the end of each year for five years. The credit union pays 5% compounded annually. At the end of five years, immediately following his fifth deposit, how much will he have in his account?
A=$500, i=5%, n=5
Year Principal Interest (5%)
Amount owned
Amount paid USD
500
1 USD
25
USD 525
2 USD
26
USD 551
3 USD
28
USD 579
4 USD
29
USD 608
5 USD
30 USD
638 USD
638
So, the amount of money owned by the man after 5 years is 638 US Dollar.
2. On January 1, a man deposits $5000 in a credit union that pays 8% interest compounded annually. He wishes to withdraw all the money in five equal end of year sum, beginning December 31st of the first year. How should he withdraw each year?
Year Principal Interest (8%)
Amount owned
Amoun t paid $
5.000
1 $
400 $
5.400
2 $
432 $
5.832
3 $
467 $
6.299
4 $
504
$ 6.802
5 $
544
$ 7.347
$ 7.347
The withdrawal for each year would be $5400 for year 1, $5832 for year 2, $6299 for year 3, $6802 for year 4, and $7347 for year 5.
3. Consider the following cash flow diagram if the interest rate is 12%, calculate the P value
!
P = A(1+ i)-1 + A(1+ i)-2 + ……+ A(1 + i)-n
=(6000*(1+12)^-1)+(10000*(1+12)^-2)+(3000*(1+12)^-3)+(12000*(1+12)^- 4)+(8000*(1+12)^-5
= $522,52
So, the P value is $522,52.
4. The amount of money that must be saved from next year to the 6th year in the same amount so that at the end of the 10th year, the money collected is Rp. 20 million (if i = 10% / year ) is?
=20000000*(10/(((1+10)^10)-1))
= $522,52
5. If you save your money in a bank from next year to the 5th year of Rp. 20 million per year, how much money will you get in year 10th?
N1=5 N2=10
F1=20000000
It means, there’s no “i”. And we can assume with common sense presumption, that the P value is 10000000. And the A cumulative after 5 years is 10000000. So, the interest for each year valued about 10000000/5=2000000. If we stretch it to 10 years, means that the additional cumulative interest would be valued about 2000000x5=10000000. Then, the value after 10 years would be 20000000+10000000=30000000.
6. A man purchased a new automobile. He wishes to set aside enough money in a bank account to pay the maintenance on the car for the first five years. It has been estimated that the maintenance cost of an automobile for the first year is $120 and will increase
$300 each year. Assume the maintenance costs occur at the end of each year and that the bank pays 5% interest. How much should he deposit in the bank now?
A1 120
G 300
i 5
n 5
Pt=120(P/A,5,5)+300(P/G,5,5)
(P/A,5,5)= 120*((((1+5)^5)-1)/(5*((1+5)^5)))
=23,99691358
(P/G,5,5)= (300/5)*((((1+5)^5)-1)/(5*((1+5)^5)))-(5/((1+5)^5))
=11,99781379
Pt=120*23,99691358+300*11,99781379
=8638,811728 Note:
So, the money that has to be deposited is $8638,811728.
