2) x(1+r)^2-x=832...............eq 1
x2r=800..................... eq 2
eq1- eq2 gives xr^2=32 or x=32/r^2
substitute x value in eqn 2
32*2*r/r^2=800
or r =64/800 or 8%
Again putting 8% in eqn 2 we can determine X
x*2*0.08=800
or x=5000
I would like anyone to everyone to look into these problems & explain the solution:
1) A sum of Rs 550 was taken as a loan. This is to be paid back in two equal instalments. If the rate if interest be 20% compounded annually, then the value of each instalment is :
a) 421 b) 396 c) 360 d) 350
2) The compound interest on a certain sum for 2 year is Rs 832 and simple interest is Rs 800. Find the sum and the rate percent
3) The difference between the second and the third years interest in a certain sum at 5% compound interest is Rs 5.25. Find the sum.
4)A person borrows two equal sums at the same time at 5 and 4 percent respectively and finds that if he repays the former sum with simple interest on a certain date 6 months before the latter, he will hace to pay in each case the same amount, Rs 1100, Find the amount borrowed
a) Rs 850 b) Rs 1000 c) Rs 995 d) Rs 990
5) Find the effective annual rate corresponding to a nominal rate of 6 percent per anum, payable half-yearly
a) Rs 20.63 b) Rs 21.94 c) Rs 23.69 d) Rs 25
6) Which among the following two offers is a better one:
A) Investing an amount compounded annually at 1% per annum for 100 years
B) Investing the amount compounded annually at 100% per annum for 1 year
I am looking forward for the solutions
Q1 :
The period of loan repayment is not mentioned. Assuming that the loan will be reurned in two years,
Compounded value after two years = 550(1 + 20/100)^2 = 792
Each instalment = 792/2 = 396
Hence B.
Q3:
Let a be the principal.
Second year's interest = a(1+1/20)^2 - a(1 + 1/20)
Third year's interest = a(1+1/20)^3 - a(1 + 1/20)^2
Difference = a(1+1/20)^3 - 2a(1 + 1/20)^2 + a(1 + 1/20)
= 21a/8000
So 21a/8000 = 5.25
a = 2000
So the sum is 2000.
Q6 :
A) Investing an amount compounded annually at 1% per annum for 100 years
(1 +.01)^100 = 2.7
B) Investing the amount compounded annually at 100% per annum for 1 year
(1 +1 ) = 2
So first option is better.
Q4 is not clear since it is not indicated that the other amount has been borrowed on simple or compound interest.
Q5 is also not clear because the interest rate should be in percentage but the options are in Rs.
Last edited by 12rk34; 03-19-2009 at 12:04 PM.
This is incorrect because the principal is reduced after the first payment. Here is how to solve it.
Let:
I1=interest paid in the first payment
I2=interest paid in the second payment
P1=principal paid in the first payment
P2=principal paid in the second payment
Because the payments are equal:
I1 + P1 = I2 + P2
Because all the principal is paid:
P1 + P2 = 550
First payment interest is on the full loan:
I1 = 550 x 0.2 = 110
Second payment interest is only on the remaining principal:
I2 = (550-P1) x 0.2
Substituting:
110 + P1 = (550 - P1)(0.2) + (550-P1)
110 + P1 = 110 - 0.2P1 + 550 - P1
2.2P1 = 550
P1 = 250
Payment = 250 + 110 = 360
Check:
P2 = 550 - P1 = 550 - 250 = 300
I2 = 0.2 x 300 = 60
Payment = 300 + 60 = 360
Paul
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