Test Mid D42007dstjawaban

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MIDLE TEST Matematika Keuangan I-D4 Akuntansi Manajerial. Nopember 2009 90 menit

A Problem 1.

Investor I deposit at Bank A and Bank B 10 million and 15 million respectively. He got total interest amount Rp 230,000/month. Investor II deposit at Bank A and Bank B 20 million and 20 million respectively. He got total interest amount Rp 360,000/month. Investor III also deposit at the same banks. He deposit at Bank A 5 million less than his deposit at bank B. He got total interest amount Rp 500,000/month. Find the value of his deposit at Bank A and B respectively? Answer. Step I. (Find interest rate at bank A and bank B) Let X=interest rate at bank A and Y= interest rate at bank B Then, (1) … 10000000 X + 15000000Y

= 230000

x4

(2) ….20000000 X + 20000000Y = 360000 -20000000 X = - 160000 X = 0.008 =0.8%

x3

(1) … 10000000 x 0.8% + 15000000Y = 230000 80000 +15000000Y = 230000 15000000Y = 150000 Y = 0.01=1%

Step II (Find deposit of the investor III) Let: M = the value of Investor III deposit at bank A) N = the value of Investor III deposit at bank B M= N- 5000000 Then,

0.8% M + 1% N = 500,000 0.8% (N-5000000) + 1% N = 500000 0.8% N – 40000+1%N=500000 1.8% N=540000 18/1000 N= 540000 N=30,000,000 M=30,000,000-5,000,000=25,000,000 So, the value of Investor III deposit at bank A and bank B are 25 millions and 30 millions respectively. Problem 2

Let Total Revenue described by a linear function: Y =a X Total Cost : Y = b X + c Given : if quantity of product (X) is 200 units then Loss=1.5 millions. If quantity of product (X) is 300 units then Profit = 1.5 millions. If quantity of product (X) is 350 units then Total Cost = Rp 21.5 millions. a. Find the break even Point b.Draw the graph Answer: Step I (Find the value of a,b, and c) Profit = Total revenue –total cost = a X –( bX + c) = aX –bX –c Then, (1) ...200 a -200 b – c = -1,500,000 x3 (2) ...300 a -300b –c = 1,500,000 x 2 -c = -4,500,000 -3,000,000 -c = -7,500,000 c = 7,500,000 (3) For x=350 then Total Cost = Rp 21,500,000 350 b + c = 21,500,000 350 b +7,500,000=21,500,000 350 b = 21,500,000 – 7,500,000 350 b = 14,000,000

b=40,000 Find the value of a (1) ...200 a -200 x 40000 –7,500,000 200 a = -1,500,000 + 8,000,000+7,500,000=14,000,000 a=70,000

= -1,500,000

Find BEP Total Revenue(TR) =Total Cost(TC) 700000 X = 40000 X +7,500,000 (70000-40000) X -7,500,000 30000 X=7,500,000 X=250

Problem 3 , A man invested his money Rp 20,000,000 at a bank at 0.8% compounded monthly. Four months later the bank increase the interest rate to 0.9% per month. Seven months after the bank pay interest 0.9% per month, the man added his investment Rp 10,000,000. Find total amount of his investment for 2 years?

Answer P=20,000,000. P1=10,000,000

T1=4, i1=0.8%, t2=7, i2=0.9%, t3=13, i2=0.9% Then, P24= (20,000,000(1+0.008)4(1+0.009)7+ 10,000,000)( (1+0.009)13= 35,935,227 Problem 4

Suppose we invest at a bank at an interest rate compounded monthly. For 4 months the total amount is Rp 825,908.84 and for 8 months the total amount is Rp 852,656.77. Find the total amount of the investment for a year. Answer Step 1. Find the value of P and i P (1+i)8 =852,656.77 P (1+i)4 =825,908.84 ___________________ : (1+i)8-4 =852,656.77/825,908.84 (1+i) 4 = 852,656.77/825,908.84 (1+i) = 1,032386 1+i= 1.008 then i=0.008=0.8% 4

Find P P (1+0.008)8 =852,656.77 P=852,656.77/ (1+0.008)8 P=800,000 Find P12 P12 = 800,000 (1+0.008)12 = 880,270.955

B Problem 1.

Investor I deposit at Bank A and Bank B 20 million and 15 million respectively. He got total interest amount Rp 370,000/month. Investor II deposit at Bank A and Bank B 10 million and 10 million respectively. He got total interest amount Rp 210,000/month. Investor III also deposit at the same banks. He deposit at Bank A 10 million more than his deposit at bank B. He got total interest amount Rp 530,000/month. Find the value of his deposit at Bank A and B respectively? Answer. Step I. (Find interest rate at bank A and bank B) Let X=interest rate at bank A and Y= interest rate at bank B Then, (1) … 20000000 X + 15000000Y = 370000 (2) ….10000000 X + 10000000Y = 210000 10000000 X = 110000 X = 0.011 =1.1%

x2 x3

(1) … 20000000 x 1.1% + 15000000Y = 370000 220000 +15000000Y = 150000 15000000Y = 150000

Y

= 0.01=1%

Step II (Find deposit of the investor III) Let: M = the value of Investor III deposit at bank A) N = the value of Investor III deposit at bank B M= N+ 10000000 Then,

1.1% M + 1% N = 530,000 1.1% (N+10000000) + 1% N = 530000 1.1% N + 110000+1%N=530000 2.1% N=420000 21/1000 N= 420000 N=20,000,000 M=20,000,000+10,000,000=30,000,000 So, the value of Investor III deposit at bank A and bank B are 30 millions and 20 millions respectively. Problem 2

Let Total Revenue described by a linear function: Y =a X Total Cost : Y = b X + c Given : if quantity of product (X) is 100 units then Loss=2 millions. If quantity of product (X) is 200 units then Profit = 2 millions. If quantity of product (X) is 250 units then Total Cost = Rp 18.5 millions. a. Find the break even Point

b.Draw the graph Ans 50000, 90000 , 6milions, BP=150 Answer: Step I (Find the value of a,b, and c) Profit = Total revenue –total cost = a X –( bX + c) = aX –bX –c Then, (1) ...100 a -100 b – c = -2,000,000 x2 (2) ...200 a -200b –c = 2,000,000 x1 -c = -4,000,000 -2,000,000 -c = -6,000,000 c = 6,000,000 (3) For x=250 then Total Cost = Rp 18,500,000 250 b + c = 18,500,000 250 b +6,000,000=18,500,000 250 b = 18,500,000 – 6,000,000 250 b = 12,500,000 b=50,000 Find the value of a (1) ...100 a -100 x 50000 –6,000,000 100 a = -2,000,000 + 5,000,000+6,000,000=9,000,000 a=90,000

= -2,000,000

Find BEP Total Revenue(TR) =Total Cost(TC) 900000 X = 50000 X +6,000,000 (90000-50000) X -6,000,000 40000 X=6,000,000 X=150

Problem 3 , A man invested his money Rp 10,000,000 at a bank at 0.7% compounded monthly. Five months later the bank decrease the interest rate to 0.6% per month. Eight months after the bank pay interest 0.6% per month, the man withdraw his investment Rp 5,000,000. Find total amount of his investment for 2 years?

Answer P=10,000,000. P1=5,000,000 T1=5, i1=0.7%, t2=8, i2=0.6%, t3=11, i2=0.6% Then, P24= (10,000,000(1+0.007)5(1+0.006)85,000,000)( (1+0.006)11= 6.261.282

Problem 4

Suppose we invest at a bank at an interest rate compounded monthly. For 3 months the total amount is Rp 919,032.61 and for 9 months the total amount is Rp 958,313.80. Find the total amount of the investment for a year. 900000, 0.7%

Answer Step 1. Find the value of P and i P (1+i)9 =958,313.80 P (1+i)3 =919,032.61 ___________________ : (1+i)9-3 =958,313.80/919,032.61 (1+i) 6 = 958,313.80/919,032.61 (1+i) = 1,0427419 1+i= 1.007 then i=0.007=0.7% 6

Find P P (1+0.007)9 =958,313.80 P=958,313.80/ (1+0.007)9

P=900,000 Find P12 P12 = 900,000 (1+0.007)12 = 978579,59