Homework 3 Ektek [PDF]

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Homework #3 Question : 1. What uniform annual amount would you have to deposit for 5 year to have an equivalent present-investment sum of Rp. 100M at an interest rate of 1.5 % per month compounded continuously? 2. A student borrowed Rp. 8.5M from a bank to buy a computer with an agreement to repay Rp 250K at the end of the month of each of the first 2 years and Rp. 3.5M at the end of the second year. Determine the rate of interest (effective monthly, nominal, and effective annually) that makes the receipts and disbursement equal? 3. A cash flow at 1.5% per month interest compounded semiannually consists of: 



single receipt of Rp. 23.5M at the first day of the month;







four equal receipts of Rp. 3.50M starting from the end of the third month;







two equal disbursements of Rp 2.75M each at the end of the fourth and fifth month;







single payment of Rp 19.75M at the end of seventh month.



Calculate the net cash flow at the end of the year (version 1). Solution : 1. Known : i=1.5% per month P = 100 M n = 5 year Ieff per year = (1+r/m)m – 1 =(1+0.015*12/12)12-1=19.56% From equation : P= A (1+i)5-1 / i(1+i)5 100M=A(1+19,56%)5-1/19,56%(1+19,56%)5 100M=A(1,44322)/0,477938 A=33,12M Cash Flow Diagram (+)



0



1



2



3



AC = 33,12M 100M



4



5



2. Known : n=2 years=24 month 8.5M = 250K (p/A. i%, 24) +3.5 M (p/F, i%, 24) Using a numerical method to find the value of interest,and the result is i = 0.66% per month inominal=(1+0,66%)^12-1=8,21% Cash Flow diagram 8,5M



First Cost



0



1



(+)



2



3



4



5



6 ………………………………..24



AC = 250K



3,5M



3. Known : i= 1.5 % per month F = 23.5M (F/P, 1.5%, 12)+3.59M(F1/A, 1.5%, 4). (F/F1, 1.5%, 5) -2.75M(F2/A,1.5%, 2).(F/F2, 1.5%, 6) -19.75M(F/P,1.5%. 4) =23.5M(1.1956)+3.59M(4.0909)(1.0773)-2.75(2.0150)(1.0934)19.75(1.0614)=16.89M Cash Flow diagram 23,5M



0



3,59M



1



2



3



4



5



6



2,75M



F



7



8 ……………………..12 19,75M