Fundamentals of Numeric Computing
CPAN 112  Lab 03
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 What rate of interest did you receive over a period of 1yr and 60 days if your principal was $1500 and it has a maturity value of $2500?
 Principal amt = $1500
 Maturity Value = $2500
 Time = 1 yr + 60/365
 = 1.16438 yr
 Interest = 25001500 = 1000
 I = P*T*R
 R = I/P*T
 R = 1000 /(1500*1.16438)
 R = 0.57255
 R=57.26%
 What sum of money invested at 11% p.a., compounded quarterly, will grow to $7500.00 in 5 years and 9 months?
 A = 7500
 t = 5 years and 9 months (69/12 = 23/4)
 r = 11%
 A = P*(1 + r/n)n*t
 7500 = P*(1 + 0.11/4)
 4*23/4
 7500 = P*(1.0275)
 23
 7500 = P*1.8663
 P = 7500/1.8663
 P = 4018.64
 Therefore the, principal of $4018.64 will grow to 7500 in 5 years and 9 months.
 A debt of $9200 due today is to be settled by two equal payments due three months from now, and 9 months from now respectively. What is the size of the equal payments at 7% compounded quarterly?
 PV = 9200
 r = 7%
 PV = A/(1 + r/n)t
 9200 = A/(1 + 0.07/4)1 + A/(1 + 0.07/4)3
 9200 = A/(1.0175) + A/(1.0534)
 9200 = {(A*1.0534) + (A*1.0175)}/{1.0534 * 1.0175}
 9200 = 2.0709A / 1.0719
 9200*1.0719 = 2.0709A
 9,861.48 = 2.0709A
 A = 9,861.48 / 2.0709
 A = 4,761.93
 Therefore, the size of the equal payments will be $4,761.93.
 John started a registered retirement savings plan on January 1, 2008, with a deposit of $5000. He added $3500 on January 1, 2009, and $7500 on January 1,2010. What is the accumulated value of his RRSP account on July 1, 2010, if interest is 9% compounded quarterly?
 Principal amt = $5000
 rate = 9% (0.09)
 n = 4 (quarterly payments)
 t = 1 year
 A = P*(1 + r/n)n*t
 A = 5000*(1 + 0.09/4)4*1
 A = 5000*(1.0225)4
 A = 5000*1.0931
 A = 5465.5
 After a year a deposit of $3500 was made
 So, Principal = $3500 + $5465.5 = $8965.5
 Accumulated value for January 1st, 2009:
 A = P*(1 + r/n) 4*1
 A = 8965.5*(1 + 0.09/4)1*4
 A = 9800.04
 Another deposit of $7500 was made 1 year later
 So, Principal = $7500 + $9800.04 = $17,300.04
 Accumulated value for July 1st, 2010:
 t = 0.5 (Since the given time is of 6 months)
 A = P*(1 + r/n)n*t
 A = 17,300.04*(1 + 0.09/4) 4*0.5
 A = 17,300.04*(1.0225)2
 A = 17,300.04*1.0455
A = 18,087.3  Therefore, accumulated value of his RRSP account on July 1, 2010 is $18,087.3
 In ten months, you want to buy a car. You can invest $24 000 at 3.3% now. The car you want to purchase has a price of $22 225 plus $750 for freight and $1200 for air conditioning. GST of 6% is charged on all items.
 How much money will you have and is it enough?
 At the current rate of simple interest, how much longer will you have to wait?
 While you are saving for the car a new model comes out and it has 1.2% price increase. The freight and the air conditioning do not have a price increase. You will be able to afford this car if he invests money with a private lender. What rate of interest the was offered by the private lender, Use the length of time from part (b).?


 Total car price = (22,225 + 750 + 1200)* (1+0.06)
Total car price = 24,175 * 1.06
Total car price = 25,625.5
a) Investment Price = $24000
r = 3.3%
t = 10 months (10/12)
A = P*(1 + r*t)
A = 24,000*(1 + 0.033*10/12)
A = 24,000*1.0275
A = 24,660
Total money required to pay the car is $25,625.5 but we will only have
$24,660 by 10 months.
So, there will not be enough money to pay the car.
 Total car price = (22,225 + 750 + 1200)* (1+0.06)



 A = P*(1 +r*t)
25,625.5 = 24,000*(1 + 0.033 * t/12)
25,625.5/24,000 = 1 + 0.033t/12
1.0677 = 1 + 0.033t/12
1.0677 – 1 = 0.033t/12
0.0677*12 = 0.033t
t = 0.0677*12 / 0.033
t = 24.6182 months
So, they will have to wait another 24.62 – 10 = 14.62 months.
 A = P*(1 +r*t)



 New interest rate for the car =1.2%
t = 14.63 months
Car price = ((22,225*(1 + 0.012) + 750 + 1200) * (1 + 0.06))
Car price = $25,908.20
Private lender interest rate.
25,908.2 = 24,000*(1 + r/100 * 24.62/12)
25,908.2/24,000 = 1 + 2.0517r/100
1.0795 =1 + 2.0517r/100
0.0795 = 2.0517r/100
7.95 = 2.0517r
r = 3.88%
Therefore, the required interest rate is 3.88%.
 New interest rate for the car =1.2%

 A debt payment of $14000.00 due today, $5100.00 due in twenty one months, and $19000.00 due in 4.5 years are to be combined into a single payment due three years from now. What is the size of the single payment if interest is 6.50% p.a. compounded quarterly?
 r = 6.5%
 t = 36 months
 PV = FV/(1 + r/n)n*t
 1st due: 14,000
 2nd due:
 PV = 5100/(1 + 0.065/4)21/3
 PV = 5000/1.1194
 PV = $4555.8169
 3rd due:
 FV = 19000/(1 + 0.065/4)54/3
 FV = 19000/(1.3366)
 FV = 14214.8914
 Single payment:
 14000 + 4555.8169 + 14214.8914= x/(1 + 0.065/4)36/3
 32770.7083= x/1.2134
 x = 39764.23
 Therefore, the size of the single payment would be $39,764.23