Simple Interest and Compound Interest — Exercise 8(B)

Find the amount and the compound interest on ₹ 5,000 for 2 years at 8% per annum compounded annually.

Answer

Principal for the first year = ₹ 5,000

Interest for the first year = ₹ $\left(\dfrac{5000 \times 8 \times 1}{100}\right)$ = ₹ 400

Amount at the end of the first year = ₹ (5,000 + 400) = ₹ 5,400

Principal for the second year = ₹ 5,400

Interest for the second year = ₹ $\left(\dfrac{5400 \times 8 \times 1}{100}\right)$ = ₹ 432

Amount at the end of the second year = ₹ (5,400 + 432) = ₹ 5,832

∴ Amount = ₹ 5,832

Compound Interest = (Amount) − (Principal) = ₹ (5,832 − 5,000) = ₹ 832

Hence, amount = ₹ 5,832 and compound interest = ₹ 832.

Find the amount and the compound interest on ₹ 8,000 for 2 years at 6% per annum compounded annually.

Answer

Principal for the first year = ₹ 8,000

Interest for the first year = ₹ $\left(\dfrac{8000 \times 6 \times 1}{100}\right)$ = ₹ 480

Amount at the end of the first year = ₹ (8,000 + 480) = ₹ 8,480

Principal for the second year = ₹ 8,480

Interest for the second year = ₹ $\left(\dfrac{8480 \times 6 \times 1}{100}\right)$ = ₹ 508.80

Amount at the end of the second year = ₹ (8,480 + 508.80) = ₹ 8,988.80

∴ Amount = ₹ 8,988.80

Compound Interest = (Amount) − (Principal) = ₹ (8,988.80 − 8,000) = ₹ 988.80

Hence, amount = ₹ 8,988.80 and compound interest = ₹ 988.80.

Find the amount and the compound interest on ₹ 2,500 for 2 years, compounded annually, the rate of interest being 6% during the first year and 8% during the second year.

Answer

Principal for the first year = ₹ 2,500

Interest rate during first year = 6% p.a.

Interest for the first year = ₹ $\left(\dfrac{2500 \times 6 \times 1}{100}\right)$ = ₹ 150

Amount at the end of the first year = ₹ (2,500 + 150) = ₹ 2,650

Principal for the second year = ₹ 2,650

Interest rate during second year = 8% p.a.

Interest for the second year = ₹ $\left(\dfrac{2650 \times 8 \times 1}{100}\right)$ = ₹ 212

Amount at the end of the second year = ₹ (2,650 + 212) = ₹ 2,862

∴ Amount = ₹ 2,862

Compound Interest = (Amount) − (Principal) = ₹ (2,862 − 2,500) = ₹ 362

Hence, amount = ₹ 2,862 and compound interest = ₹ 362.

Find the amount and the compound interest on ₹ 25,000 for 3 years at 6% per annum compounded annually.

Answer

Principal for the first year = ₹ 25,000

Interest for the first year = ₹ $\left(\dfrac{25000 \times 6 \times 1}{100}\right)$ = ₹ 1,500

Amount at the end of the first year = ₹ (25,000 + 1,500) = ₹ 26,500

Principal for the second year = ₹ 26,500

Interest for the second year = ₹ $\left(\dfrac{26500 \times 6 \times 1}{100}\right)$ = ₹ 1,590

Amount at the end of the second year = ₹ (26,500 + 1,590) = ₹ 28,090

Principal for the third year = ₹ 28,090

Interest for the third year = ₹ $\left(\dfrac{28090 \times 6 \times 1}{100}\right)$ = ₹ 1,685.40

Amount at the end of the third year = ₹ (28,090 + 1,685.40) = ₹ 29,775.40

∴ Amount = ₹ 29,775.40

Compound Interest = (Amount) − (Principal) = ₹ (29,775.40 − 25,000) = ₹ 4,775.40

Hence, amount = ₹ 29,775.40 and compound interest = ₹ 4,775.40.

Find the amount and the compound interest on ₹ 10,000 for 3 years at 10% per annum compounded annually.

Answer

Principal for the first year = ₹ 10,000

Interest for the first year = ₹ $\left(\dfrac{10000 \times 10 \times 1}{100}\right)$ = ₹ 1,000

Amount at the end of the first year = ₹ (10,000 + 1,000) = ₹ 11,000

Principal for the second year = ₹ 11,000

Interest for the second year = ₹ $\left(\dfrac{11000 \times 10 \times 1}{100}\right)$ = ₹ 1,100

Amount at the end of the second year = ₹ (11,000 + 1,100) = ₹ 12,100

Principal for the third year = ₹ 12,100

Interest for the third year = ₹ $\left(\dfrac{12100 \times 10 \times 1}{100}\right)$ = ₹ 1,210

Amount at the end of the third year = ₹ (12,100 + 1,210) = ₹ 13,310

∴ Amount = ₹ 13,310

Compound Interest = (Amount) − (Principal) = ₹ (13,310 − 10,000) = ₹ 3,310

Hence, amount = ₹ 13,310 and compound interest = ₹ 3,310.

Karim took a loan of ₹ 25,000 from Corporation Bank at 12% per annum, compounded annually. How much amount, he will have to pay at the end of 3 years?

Answer

Principal for the first year = ₹ 25,000

Interest for the first year = ₹ $\left(\dfrac{25000 \times 12 \times 1}{100}\right)$ = ₹ 3,000

Amount at the end of the first year = ₹ (25,000 + 3,000) = ₹ 28,000

Principal for the second year = ₹ 28,000

Interest for the second year = ₹ $\left(\dfrac{28000 \times 12 \times 1}{100}\right)$ = ₹ 3,360

Amount at the end of the second year = ₹ (28,000 + 3,360) = ₹ 31,360

Principal for the third year = ₹ 31,360

Interest for the third year = ₹ $\left(\dfrac{31360 \times 12 \times 1}{100}\right)$ = ₹ 3,763.20

Amount at the end of the third year = ₹ (31,360 + 3,763.20) = ₹ 35,123.20

Hence, Karim will have to pay ₹ 35,123.20 at the end of 3 years.

Manoj deposited ₹ 15,625 in a bank at 8% per annum, compounded annually. How much amount will he get after 3 years?

Answer

Principal for the first year = ₹ 15,625

Interest for the first year = ₹ $\left(\dfrac{15625 \times 8 \times 1}{100}\right)$ = ₹ 1,250

Amount at the end of the first year = ₹ (15,625 + 1,250) = ₹ 16,875

Principal for the second year = ₹ 16,875

Interest for the second year = ₹ $\left(\dfrac{16875 \times 8 \times 1}{100}\right)$ = ₹ 1,350

Amount at the end of the second year = ₹ (16,875 + 1,350) = ₹ 18,225

Principal for the third year = ₹ 18,225

Interest for the third year = ₹ $\left(\dfrac{18225 \times 8 \times 1}{100}\right)$ = ₹ 1,458

Amount at the end of the third year = ₹ (18,225 + 1,458) = ₹ 19,683

Hence, Manoj will get ₹ 19,683 after 3 years.

A person lent out ₹ 16,000 on simple interest and the same sum on compound interest for 2 years at $12\dfrac{1}{2}$% per annum. Find the ratio of the amounts received by him as interest after 2 years.

Answer

Here,

P = ₹ 16,000, R = $12\dfrac{1}{2}$% p.a. = $\dfrac{25}{2}$% p.a. and T = 2 years.

For simple interest :

S.I. = $\dfrac{\text{P} \times \text{R} \times \text{T}}{100}$

$= ₹ \left(16000 \times \dfrac{25}{2} \times 2 \times \dfrac{1}{100}\right)$ = ₹ 4,000

For compound interest :

Principal for the first year = ₹ 16,000

Interest for the first year = ₹ $\left(16000 \times \dfrac{25}{2} \times \dfrac{1}{100}\right)$ = ₹ 2,000

Amount at the end of the first year = ₹ (16,000 + 2,000) = ₹ 18,000

Principal for the second year = ₹ 18,000

Interest for the second year = ₹ $\left(18000 \times \dfrac{25}{2} \times \dfrac{1}{100}\right)$ = ₹ 2,250

Amount at the end of the second year = ₹ (18,000 + 2,250) = ₹ 20,250

C.I. = (Amount) − (Principal) = ₹ (20,250 − 16,000) = ₹ 4,250

∴ S.I. : C.I. = 4000 : 4250 = 16 : 17

Hence, the required ratio is 16 : 17.