Lesson 7 Simple Interest
Exercise 7.1
1. Write very short answers to the following questions.a) What is interest?
The additional money deposited in principal after a fixed time is called interest.
b) What is Principal?
The amount borrowed or lent or the sum of money deposited in the bank is called principal.
c) Write 30 months in years.
= 30/12 years
= 2.5 years Ans
2. Find the simple interest by using the unitary method.a) Principal = Rs. 500, Rate of interest (R) = 10%, Time = 3 years
Solution:
Here, according to the meaning of 10% rate of interest per year:
The interest of Rs. 100 for 1 year = 10
The interest of Rs. 1 for 1 year = 10/100
The interest of Rs. 500 for 1 year = (10/100) x 500
The interest of Rs. 500 for 3 years = (10/100) x 500 x 3
= Rs. 150
Therefore, the simple interest is Rs. 150.
b) Principal = Rs. 5,200, Rate of interest (R) = 12%, Time = 5 years
Solution:
Here, according to the meaning of 12% rate of interest per year:
The interest of Rs. 100 for 1 year = 12
The interest of Rs. 1 for 1 year = 12/100
The interest of Rs. 5,200 for 1 year = (12/100) x 5200
The interest of Rs. 5,200 for 5 years = (12/100) x 5200 x 5
= Rs. 3,120
Therefore, the simple interest is Rs. 3,120.
c) Principal = Rs. 3,300, Rate of interest (R) = 7.5%, Time = 3 years 6 months
Solution:
Here, according to the meaning of 7.5% rate of interest per year:
The interest of Rs. 100 for 1 year = 7.5
The interest of Rs. 1 for 1 year = 7.5/100
The interest of Rs. 3,300 for 1 year = (7.5/100) x 3300
The interest of Rs. 3,300 for 3 years 6 months = (7.5/100) x 3300 x 3.5
= Rs. 866.25
Therefore, the simple interest is Rs. 866.25.
d) Principal = Rs. 1,200, Rate of interest (R) = 3%, Time = 3 years 3 months
Solution:
Here, according to the meaning of 3% rate of interest per year:
The interest of Rs. 100 for 1 year = 3
The interest of Rs. 1 for 1 year = 3/100
The interest of Rs. 1,200 for 1 year = (3/100) x 1200
The interest of Rs. 1,200 for 3 years 3 months = (3/100) x 1200 x 3.25
= Rs. 117
Therefore, the simple interest is Rs. 117.
3. Find the time T.(a) Principal = Rs. 1,260, Rate of interest (R) = 5%, Interest (I) = Rs. 378
Solution:
Principal (P) = Rs. 1,260
Rate of interest (R) = 5%
Interest (I) = Rs. 378
Time (T) = ?
We know that,
T = I × 100 / P × R
= 378 × 100 / 1260 × 5
= 37800 / 6300
= 6 years
Therefore, the time is 6 years.
(b) Principal = Rs. 1,250, Rate of interest (R) = 13%, Interest (I) = Rs. 650
Solution:
Principal (P) = Rs. 1,250
Rate of interest (R) = 13%
Interest (I) = Rs. 650
Time (T) = ?
We know that,
T = I × 100 / P × R
= 650 × 100 / 1250 × 13
= 65000 / 16250
= 4 years
Therefore, the time is 4 years.
(c) Principal = Rs. 4,500, Rate of interest (R) = 4%, Interest (I) = Rs. 900
Solution:
Principal (P) = Rs. 4,500
Rate of interest (R) = 4%
Interest (I) = Rs. 900
Time (T) = ?
We know that,
T = I × 100 / P × R
= 900 × 100 / 4500 × 4
= 90000 / 18000
= 5 years
Therefore, the time is 5 years.
4. Find the Interest rate R.(a) Principal = Rs. 7,200, Time (T) = 5 years, Interest = Rs. 1,080
Solution:
Principal (P) = Rs. 7,200
Time (T) = 5 years
Interest (I) = Rs. 1,080
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 1080 × 100 / 7200 × 5
= 108000 / 36000
= 3%
Therefore, the interest rate is 3%.
(b) Principal = Rs. 6,000, Time (T) = 3 years 6 months, Interest = Rs. 1,155
Solution:
Principal (P) = Rs. 6,000
Time (T) = 3.5 years
Interest (I) = Rs. 1,155
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 1155 × 100 / 6000 × 3.5
= 115500 / 21000
= 5.5%
Therefore, the interest rate is 5.5%.
(c) Principal = Rs. 2,160, Time (T) = 4 years, Interest = Rs. 648
Solution:
Principal (P) = Rs. 2,160
Time (T) = 4 years
Interest (I) = Rs. 648
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 648 × 100 / 2160 × 4
= 64800 / 8640
= 7.5%
Therefore, the interest rate is 7.5%.
4. Find the Interest rate R.(a) Principal = Rs. 7,200, Time (T) = 5 years, Interest = Rs. 1,080
Solution:
Principal (P) = Rs. 7,200
Time (T) = 5 years
Interest (I) = Rs. 1,080
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 1080 × 100 / 7200 × 5
= 108000 / 36000
= 3%
Therefore, the interest rate is 3%.
(b) Principal = Rs. 6,000, Time (T) = 3 years 6 months, Interest = Rs. 1,155
Solution:
Principal (P) = Rs. 6,000
Time (T) = 3.5 years
Interest (I) = Rs. 1,155
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 1155 × 100 / 6000 × 3.5
= 115500 / 21000
= 5.5%
Therefore, the interest rate is 5.5%.
(c) Principal = Rs. 2,160, Time (T) = 4 years, Interest = Rs. 648
Solution:
Principal (P) = Rs. 2,160
Time (T) = 4 years
Interest (I) = Rs. 648
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 648 × 100 / 2160 × 4
= 64800 / 8640
= 7.5%
Therefore, the interest rate is 7.5%.
5. Find the principal P.(a) Rate of interest (R) = 9%, Time (T) = 9 years, Interest = Rs. 810
Solution:
Rate of interest (R) = 9%
Time (T) = 9 years
Interest (I) = Rs. 810
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 810 × 100 / 9 × 9
= 81000 / 81
= Rs. 1,000
Therefore, the principal is Rs. 1,000.
(b) Rate of interest (R) = 4.8%, Time (T) = 1 month, Interest = Rs. 3,996
Solution:
Rate of interest (R) = 4.8%
Time (T) = 1 month = 1/12 years
Interest (I) = Rs. 3,996
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 3996 × 100 / 4.8 × (1/12)
= 399600 / 0.4
= Rs. 9,99,000
Therefore, the principal is Rs. 9,99,000.
(c) Rate of interest (R) = 6 2/3% = 20/3%, Time (T) = 5 years, Interest = Rs. 400
Solution:
Rate of interest (R) = 20/3%
Time (T) = 5 years
Interest (I) = Rs. 400
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 400 × 100 / (20/3) × 5
= 40000 × 3 / 100
= Rs. 1,200
Therefore, the principal is Rs. 1,200.
5. Find the principal P.(a) Rate of interest (R) = 9%, Time (T) = 9 years, Interest = Rs. 810
Solution:
Rate of interest (R) = 9%
Time (T) = 9 years
Interest (I) = Rs. 810
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 810 × 100 / 9 × 9
= 81000 / 81
= Rs. 1,000
Therefore, the principal is Rs. 1,000.
(b) Rate of interest (R) = 4.8%, Time (T) = 1 month, Interest = Rs. 3,996
Solution:
Rate of interest (R) = 4.8%
Time (T) = 1 month = 1/12 years
Interest (I) = Rs. 3,996
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 3996 × 100 / 4.8 × (1/12)
= 399600 / 0.4
= Rs. 9,99,000
Therefore, the principal is Rs. 9,99,000.
(c) Rate of interest (R) = 6 2/3% = 20/3%, Time (T) = 5 years, Interest = Rs. 400
Solution:
Rate of interest (R) = 20/3%
Time (T) = 5 years
Interest (I) = Rs. 400
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 400 × 100 / (20/3) × 5
= 40000 × 3 / 100
= Rs. 1,200
Therefore, the principal is Rs. 1,200.
6. If Ganga deposited a sum of Rs. 3,500 in Nepal Bank Limited at a 7% rate of interest for 4 years, calculate the interest she will get from the bank?Solution:
Principal (P) = Rs. 3,500
Rate of interest (R) = 7%
Time (T) = 4 years
Interest (I) = ?
We know that,
I = P × T × R / 100
= 3500 × 7 × 4 / 100
= Rs. 980
Therefore, the interest Ganga will get is Rs. 980.
7. If Sandesh borrowed a loan of Rs. 18,000 from a bank at a 6.6% rate of interest per year, how much interest should he pay after 30 months?Solution:
Principal (P) = Rs. 18,000
Rate of interest (R) = 6.6%
Time (T) = 30 months = 2.5 years
Interest (I) = ?
We know that,
I = P × T × R / 100
= 18000 × 6.6 × 2.5 / 100
= Rs. 2970
Therefore, the interest Sandesh should pay is Rs. 2,970.
8. Bhargav received Rs. 550 interest on a certain sum of money after 4 years. If he got the interest at a 5.5% rate of interest on that sum, then find the sum deposited by him?Solution:
Interest (I) = Rs. 550
Rate of interest (R) = 5.5%
Time (T) = 4 years
Principal (P) = ?
We know that,
P = I × 100 / R × T
= 550 × 100 / 5.5 × 4
= 55000 / 22
= Rs. 2,500
Therefore, the sum deposited by Bhargav is Rs. 2,500.
9. If a bank gave Rs. 1,254 to Sarisma as the interest after 3 years for the deposit of Rs. 7,600, then find the rate of interest?Solution:
Interest (I) = Rs. 1,254
Principal (P) = Rs. 7,600
Time (T) = 3 years
Rate of interest (R) = ?
We know that,
R = I × 100 / P × T
= 1254 × 100 / 7600 × 3
= 125400 / 22800
= 5.5%
Therefore, the rate of interest is 5.5%.
10. How many years will Rs. 900 need to be deposited at the interest rate of 12% to get the amount equal to the interest of Rs. 1,080 in 4 years at the interest rate of 10%?Solution:
Principal (P) = Rs. 1,080
Rate of interest (R) = 10%
Time (T) = 4 years
We use the formula:
I = (P × T × R) / 100
or, I = (1080 × 10 × 4) / 100
or, I = Rs. 432
Now, let's find the time (T) for Rs. 900 at 12% to accumulate the same interest (Rs. 432):
Interest (I) = Rs. 432
Principal (P) = Rs. 900
Rate (R) = 12%
Time (T) = ?
Using the formula:
I = (P × T × R) / 100
or, 432 = (900 × T x 12) / 100
or, 432 = 10800 × T / 100
or, 432 = 108 × T
or, T = 432 / 108
or, T = 4 years
Therefore, the time required is 4 years.
Exercise 7.2
1. Find the amount A:
(a)
Solution:
Principal (P) = Rs. 50,000
Rate of interest (R) = 3%
Time (T) = 7 years
Amount (A) = P + I
Interest (I) = PTR/100
= 50,000 x 7 x 3 / 100
= Rs. 10,500
Now, Amount (A) = P + I
= 50,000 + 10,500
= Rs. 60,500
So, Interest = Rs. 10,500 and Amount = Rs. 60,500
(b)
Solution:
Principal (P) = Rs. 2,160
Rate of interest (R) = 3.5%
Time (T) = 4 years
Amount (A) = P + I
Interest (I) = PTR/100
= 2,160 x 4 x 3.5 / 100
= Rs. 302.40
Now, Amount (A) = P + I
= 2,160 + 302.40
= Rs. 2,462.40
So, Interest = Rs. 302.40 and Amount = Rs. 2,462.40
(c)
Solution:
Principal (P) = Rs. 55,500
Rate of interest (R) = 7.5%
Time (T) = 2 years
Amount (A) = P + I
Interest (I) = PTR/100
= 55,500 x 2 x 7.5 / 100
= Rs. 8,325
Now, Amount (A) = P + I
= 55,500 + 8,325
= Rs. 63,825
So, Interest = Rs. 8,325 and Amount = Rs. 63,825
(d)
Solution:
Principal (P) = Rs. 5,24,000
Rate of interest (R) = 11%
Time (T) = 3 months = 3/12 years = 0.25 years
Amount (A) = P + I
Interest (I) = PTR/100
= 5,24,000 x 0.25 x 11 / 100
= Rs. 14,420
Now, Amount (A) = P + I
= 5,24,000 + 14,420
= Rs. 5,38,420
So, Interest = Rs. 14,420 and Amount = Rs. 5,38,420
2. Aruna took Rs 200,000 at 12% interest rate from a bank for cow husbandry. If she paid the amount including interest after 30 months, then how much did she pay in total?
Solution:
Principal (P) = Rs. 200,000
Rate of interest (R) = 12%
Time (T) = 30 months = 30/12 years = 2.5 years
Amount (A) = P + I
Interest (I) = PTR/100
= 200,000 x 2.5 x 12 / 100
= Rs. 60,000
Now, Amount (A) = P + I
= 200,000 + 60,000
= Rs. 260,000
So, Interest = Rs. 60,000 and Total Amount = Rs. 260,000
3. What will be the amount if Rs 35,000 is deposited at 3% interest rate for 54 months?
Solution:
Principal (P) = Rs. 35,000
Rate of interest (R) = 3%
Time (T) = 54 months = 54/12 years = 4.5 years
Amount (A) = P + I
Interest (I) = PTR/100
= 35,000 x 4.5 x 3 / 100
= Rs. 4,725
Now, Amount (A) = P + I
= 35,000 + 4,725
= Rs. 39,725
So, Interest = Rs. 4,725 and Amount = Rs. 39,725
4. How much should be deposited in the bank at 10% interest rate to get Rs 610 as interest for 4 months?
Solution:
Interest (I) = Rs. 610
Rate of interest (R) = 10%
Time (T) = 4 months = 4/12 years = 1/3 years
Principal (P) = (I × 100) / (T × R)
= 610 × 100 / (1/3 × 10)
= Rs. 18,300
So, Principal = Rs. 18,300
5. How much sum should be deposited to get total amount Rs 251225 at 5% interest rate for 4 years 6 months?
Solution:
Amount (A) = Rs. 251225
Rate of interest (R) = 5%
Time (T) = 4.5 years
Principal (P) = A / (1 + (R × T) / 100)
= 251225 / (1 + (5 × 4.5) / 100)
= 251225 / 1.225
= Rs. 205,000
So, Principal = Rs. 205,000
6. What amount will be refunded when Rs 7,500 is deposited at 5.5% interest rate per year for 42 months?
Solution:
Principal (P) = Rs. 7,500
Rate of interest (R) = 5.5%
Time (T) = 42 months = 42/12 years = 3.5 years
Amount (A) = P + I
Interest (I) = PTR/100
= 7,500 x 3.5 x 5.5 / 100
= Rs. 1,462.50
Now, Amount (A) = P + I
= 7,500 + 1,462.50
= Rs. 8,962.50
So, Interest = Rs. 1,462.50 and Amount = Rs. 8,962.50
7. Adira saves Rs 40,000 in bank at 5% interest rate per year and she pays 5% of interest as income tax, then how much will she receive after 4 years?
Solution:
Principal (P) = Rs. 40,000
Rate of interest (R) = 5%
Time (T) = 4 years
Amount (A) = P + I
Interest (I) = PTR/100
= 40,000 x 4 x 5 / 100
= Rs. 8,000
Tax on interest = 5% of Rs. 8,000 = Rs. 400
Amount after tax = P + (Interest - Tax)
= 40,000 + (8,000 - 400)
= Rs. 47,600
So, Interest = Rs. 8,000, Tax = Rs. 400, and Amount = Rs. 47,600
8. If the bank levied 5% tax in the interest of sum Rs 75,000 at 5.6% interest rate for 6 months, then what amount will be received after 6 months?
Solution:
Principal (P) = Rs. 75,000
Rate of interest (R) = 5.6%
Time (T) = 6 months = 6/12 years = 0.5 years
Interest (I) = PTR/100
= 75,000 x 0.5 x 5.6 / 100
= Rs. 2,100
Tax on interest = 5% of Rs. 2,100 = Rs. 105
Amount after tax = P + (Interest - Tax)
= 75,000 + (2,100 - 105)
= Rs. 76,995
So, Interest = Rs. 2,100, Tax = Rs. 105, and Amount = Rs. 76,995
9. If 5% of interest on Rs 10,800 at 10% interest rate for 4 years is to be paid as tax, then what will be the total amount after 4 years?
Solution:
Principal (P) = Rs. 10,800
Rate of interest (R) = 10%
Time (T) = 4 years
Interest (I) = PTR/100
= 10,800 x 4 x 10 / 100
= Rs. 4,320
Tax on interest = 5% of Rs. 4,320 = Rs. 216
Amount after tax = P + (Interest - Tax)
= 10,800 + (4,320 - 216)
= Rs. 14,904
So, Interest = Rs. 4,320, Tax = Rs. 216, and Amount = Rs. 14,904
10. Hari borrowed a loan of Rs 300,000 at 12% interest rate for 2 years and 6 months for foreign employment.
(a)
Solution:
Principal (P) = Rs. 300,000
Rate of interest (R) = 12%
Time (T) = 2.5 years
Interest (I) = PTR/100
= 300,000 x 2.5 x 12 / 100
= Rs. 90,000
So, Interest = Rs. 90,000
(b)
Total amount = Principal + Interest
= 300,000 + 90,000
= Rs. 390,000
So, Total amount = Rs. 390,000
Solution of selected questions from Excel in Mathematics - Book 8
1. A businessman deposited Rs 60,000 in a Commercial Bank at 4.5% p.a. How long should he deposit the sum to receive an amount of Rs 61,350?
Solution:
Principal (P) = Rs 60,000; Rate of interest (R) = 4.5%; Amount (A) = Rs 61,350; Time (T) = ?
Now, Interest (I) = A - P = Rs 61,350 - Rs 60,000 = Rs 1,350
Again,
T = (I x 100) / (P x R) = Rs 1,350 x 100 / Rs 60,000 x 4.5 = 0.5 years = 12 x 0.5 months = 6 months
Hence, the required time duration is 6 months.
2. What sum of money amounts to Rs 5,454 at 8% p.a. in 30 months?
Solution:
Here, Amount (A) = Rs 5,454
Rate of interest (R) = 8% p.a.
Time (T) = 30 months = 30/12 years = 2.5 years
Principal (P) = ?
Again,
P = (A x 100) / (100 + TR) = Rs 5,454 x 100 / (100 + 2.5 x 8) = Rs 4,545
Hence, the required sum is Rs 4,545.
3. Pradeep lent a sum to Santosh at the rate of 12 1/2% p.a. After 4 years, Santosh paid him, Rs 7,500 and cleared the debt, what sum did Pradeep lend to Santosh?
Solution:
Here, Amount (A) = Rs 7,500; Rate of interest (R) = 12 1/2% p.a. = 12.5% p.a.; Time (T) = 4 years
Again,
Principal (P) = (A x 100) / (100 + TR) = Rs 7,500 x 100 / (100 + 12.5 x 4) = Rs 7,50,000 / 150 = Rs 5,000
Hence, Pradeep lent Rs 5,000 to Santosh.
4. Mr. Gurung borrowed a loan of Rs 25,000 from Mr. Pandey at 12% p.a. At the end of 3 years, if he agreed to pay Rs 26,300 with a goat to clear his debt. Find the cost of the goat.
Solution:
Principal (P) = Rs 25,000; Rate of interest (R) = 12% p.a.; Time (T) = 3 years
Now,
I = (P x T x R) / 100 = Rs 15,000 x 3 x 12 / 100 = Rs 9,000
Amount = 34,000
Again,
Let the cost of the goat be Rs x.
Then, according to the question
Rs 26,300 + x = Rs 34,000
x = Rs 34,000 - Rs 26,300 = Rs 7,700
Hence, the cost of the goat is Rs 7,700.
5. Sajina deposited Rs 20,000 at the rate of 8% p.a. in her saving account. After 2 years, she withdrew Rs 5,000 and the total interest of 2 years. How long should she keep the remaining amount to get total interest of Rs 6,800 from the beginning?
Solution:
Principal (P) = Rs 20,000; Rate of interest (R) = 8% p.a.; Time (T) = 2 years
Now, I = P × T × R / 100 = Rs 20,000 × 2 × 8 / 100 = Rs 3,200
Amount = P + I = Rs 20,000 + Rs 3,200 = Rs 23,200
At the end of 2 years, the amount of withdrawal = Rs 5,000 + Rs 3,200 = Rs 8,200
Again,
Remaining sum (P₁) = Rs 23,200 - Rs 8,200 = Rs 15,000
Total interest from the beginning = Rs 6,800
Interest for the remaining sum (I₁) = Rs 6,800 - Rs 3,200 = Rs 3,600
Rate of interest (R₁) = 8% p.a.
Time (T₁) = ?
We have,
T₁ = (I₁ × 100) / (P₁ × R₁) = Rs 3,600 × 100 / Rs 15,000 × 8 = 3 years
Hence, the remaining amount should be deposited for next 3 years.
6. A man took a loan of Rs 12,000 with simple interest for as many years as the rate of interest per year. If he paid Rs 3,000 as interest at the end of the loan period, what was the rate of interest?
Solution:
Let the rate of interest (R) = x % p.a., then the loan period (T) = x years
Principal (P) = Rs 12,000; interest (I) = Rs 3,000
Now, I = P × T × R / 100
or, Rs 3000 = Rs 12,000 × x × x / 100
or, x² = 25
or, x = √25 = 5
Hence, the rate of interest was 5% p.a.
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