Std 7 Mathematics · Chapter 10

10. Banks and Simple Interest

Step-by-step solutions to Practice Sets 40 and 41 using the simple interest formula. Maharashtra State Board (Balbharati), Grade Seven Mathematics.

Formula used: Simple interest I = P × R × T100, where P = principal, R = rate of interest (p.c.p.a.), T = time in years. Amount = Principal + Interest.

Practice Set 40

1If Rihanna deposits 1500 rupees in the school fund at 9 p.c.p.a. for 2 years, what is the total amount she will get?

P = 1500, R = 9, T = 2
I = 1500 × 9 × 2100 = 270
Amount = 1500 + 270 = 1770

Rihanna will get ₹ 1,770.

2Jethalal took a housing loan of 2,50,000 rupees from a bank at 10 p.c.p.a. for 5 years. What is the yearly interest he must pay and the total amount he returns to the bank?

Yearly interest = 250000 × 10 × 1100 = 25000
Total interest for 5 years = 25000 × 5 = 125000
Amount = 250000 + 125000 = 375000

Yearly interest is ₹ 25,000 and he returns ₹ 3,75,000 in all.

3*Shrikant deposited 85,000 rupees for 212 years at 7 p.c.p.a. in a savings bank account. What is the total interest he received at the end of the period?

P = 85000, R = 7, T = 212 = 52
I = 85000 × 7 × 5100 × 2 = 2975000200 = 14875

He received ₹ 14,875 as interest.

4At a certain rate of interest, the interest after 4 years on 5000 rupees principal is 1200 rupees. What would be the interest on 15000 rupees at the same rate of interest for the same period?

1200 = 5000 × R × 4100 = 200R
∴ R = 6
Interest on 15000 = 15000 × 6 × 4100 = 3600

The interest would be ₹ 3,600.

(Shortcut: 15000 is 3 times 5000, so the interest is 3 × 1200 = 3600.)

5If Pankaj deposits 1,50,000 rupees in a bank at 10 p.c.p.a. for two years, what is the total amount he will get from the bank?

I = 150000 × 10 × 2100 = 30000
Amount = 150000 + 30000 = 180000

Pankaj will get ₹ 1,80,000.

Practice Set 41

1If the interest on 1700 rupees is 340 rupees for 2 years the rate of interest must be ______ . (i) 12% (ii) 15% (iii) 4% (iv) 10%

340 = 1700 × R × 2100 = 34R
∴ R = 10

Answer: (iv) 10%

2If the interest on 3000 rupees is 600 rupees at a certain rate for a certain number of years, what would the interest be on 1500 rupees under the same conditions? (i) 300 rupees (ii) 1000 rupees (iii) 700 rupees (iv) 500 rupees

With the same rate and time, interest is in direct proportion to the principal. 1500 is half of 3000, so the interest is half of 600.

6003000 = x1500 ∴ x = 300

Answer: (i) 300 rupees

3Javed deposited 12000 rupees at 9 p.c.p.a. in a bank for some years, and withdrew his interest every year. At the end of the period, he had received altogether 17,400 rupees. For how many years had he deposited his money?

The 17,400 rupees he received altogether is his principal returned plus all the interest.

Total interest = 17400 − 12000 = 5400
5400 = 12000 × 9 × T100 = 1080T
∴ T = 54001080 = 5

He had deposited his money for 5 years.

Check: interest each year = 1080; 1080 × 5 = 5400.

4*Lataben borrowed some money from a bank at a rate of 10 p.c.p.a. interest for 212 years to start a cottage industry. If she paid 10250 rupees as total interest, how much money had she borrowed?

10250 = P × 10 × 5100 × 2 = P4
∴ P = 10250 × 4 = 41000

Lataben had borrowed ₹ 41,000.

5Fill in the blanks in the table.

Working

(i) I = 4200 × 7 × 3100 = 882; A = 4200 + 882 = 5082
(ii) 1200 = P × 6 × 4100 ∴ P = 1200 × 10024 = 5000; A = 5000 + 1200 = 6200
(iii) 800 = 8000 × 5 × T100 = 400T ∴ T = 2 years; A = 8000 + 800 = 8800
(iv) P = A − I = 18000 − 6000 = 12000; 6000 = 12000 × 5 × T100 = 600T ∴ T = 10 years
(v) 2400 = P × 5 × 5100 × 2 = P8 ∴ P = 19200; A = 19200 + 2400 = 21600

	Principal (₹)	Rate (p.c.p.a.)	Time	Interest (₹)	Amount (₹)
(i)	4200	7%	3 years	882	5082
(ii)	5000	6%	4 years	1200	6200
(iii)	8000	5%	2 years	800	8800
(iv)	12000	5%	10 years	6000	18000
(v)	19200	212%	5 years	2400	21600

← 9. Direct Proportion and Inverse Proportion 11. Circle →