# Thread: Simple & Compound interest problems (Guru level)

1. Good post? |

## Simple & Compound interest problems (Guru level)

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

2. Good post? |
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

3. Good post? |
3. x[(1.05)^3-1]-x[(1.05)^2-1]= 5.25
x[1.05^3-1.05^2]=5.25
x*1.05*.05=5
or x = 95

4. Good post? |
Thanks a lot for the help.. The answer for Question 3) is Rs 2000

5. Good post? |
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.

6. Good post? |
Originally Posted by 12rk34
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.
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

7. Good post? |
Originally Posted by 12rk34
Q1 :

Q6 :
A) Investing an amount compounded annually at 1% per annum for 100 years
(1 +.01)^100 = 2.7
(1 +.01)^100 = 2.7 ? (How do we get this )

Thanks

8. Good post? |
Originally Posted by ACETARGET
(1 +.01)^100 = 2.7 ? (How do we get this )

Thanks
Use calculator.

9. Good post? |
Originally Posted by sunilcyborg
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
Solution : C) back tracking : check for all ,
if take 421 then 1st yr 110 is interest => 311 Principal paid so remaining P = 550 - 311 = 239. so can be answer as (239)(1.2) not equal to 421.
if 360 then P paid 250 Rs. remaining P = 300 and 300 (1.2) =360 so answer.

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
Soluton: SI for one yr =400 , addition interest on 2nd yr = 32 rs. thus Interest on interest = 32 /400 = 8% now 8% of sum is 400 then sum is 5000.

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.
Solution:
3rd yrs = x{(1.05)^3 -(1.05)^2} = .055125 * x
2ndyr =
x{(1.05)^2 -(1.05)} = .0525 * x
thus diff = .002625 x =5.25 => x =2000

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
Solution:B
time is x then 5x =4(x+.5)
=> x = 2 thus 2 yr is the time for 5 %
check the amount using back tracking
sum is 1000
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
Solution:
Rate (1.03)2-1 =6.09% so Please check the options
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
Solution: A) as 100% for 100 yr using 1% simple interest and bcz it is compounded thus interest would be >100% so A) is better option.
No need for calculation.
I am looking forward for the solutions

10. Good post? |
Thanks a lot guys.

Paul your explanation is perfect. The answer for 1) is Rs 360.

There is 1 more solution for the same

Let the value of each instalment be x

(x/(1+(20/100)) + (x/(1+(20/100)))2 = 550

5x/6 + 25x/36 = 550 x=360