A sum of money amounts to ₹ 8820 in 1 year and to ₹ 9 , 261 in 1 1 2 years when interest is compounded semi-annually. Find the sum and the rate of interest per annum.

Let principal be R s P and rate of interest be R % per annum Interest is compounded semi anually Rate of interest = R 2 % and time = 2 half years Amount after 1 year is R s 8820 8820 = P 1 + R 2 100 2 ⇒ 8820 = P 1 + R 200 2 . . . . . ( 1 ) and amount after 1 1 2 years is R s 9261 9261 = P 1 + R 2 100 3 9261 = P 1 + R 200 3 . . . . . ( 2 ) divide equation 2 by 1 ⇒ 9261 8820 = P 1 + R 100 3 P 1 + R 100 2 ⇒ 105 100 = 1 + R 100 ⇒ R 100 = 105 100 - 1 = 5 100 ⇒ R = 5 % Now for equation 1 8820 = P 1 + 5 100 2 ⇒ 8820 = P 1 + 1 20 2 8820 = P 21 20 2 ⇒ P = 8820 × 20 21 × 20 21 ⇒ P = 84000 Hence rate of interest is 5 % per annum and principal is R s 84000

A farmer borrowed ₹ 12 , 800 from a moneylender to install a jet pump. The rate of interest is 11 1 4 % per annum compounded annually. At the end of 2 years, the farmer cleared the loan by paying ₹ 10 , 842 and a gold ring. Find the cost of the ring.

Principal ( P ) = R s 12800 Rate of interest ( R ) = 11 1 4 % per annum = 45 4 % per annum Time = 2 years Now amount after 2 years = 12800 1 + 45 4 100 2 = 12800 1 + 45 400 2 = 12800 1 + 9 80 2 ⇒ 12800 89 80 2 ⇒ 12800 × 89 80 × 89 80 ⇒ R s 15842 Farmer cleared the loan by paying R s 10842 and gold ring so cost of the ring is = R s 15842 - R s 10842 = R s 5000

E M B I B E

START UP MATHEMATICS>Chapter 13 - Compound Interest>REVIEW EXERCISES>Q 5

MEDIUM

8th CBSE

IMPORTANT

Earn 100

Kusum and Ravi borrowed $₹ 80, 000$ and $₹ 60, 000$ respectively for a period of $3$ years. Kusum paid simple interest at the rate of $20 %$ per annum, while Ravi paid compound interest at the rate of $20 %$ per annum compounded annually. Who paid more interest and by how much?

Important Questions on Compound Interest

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>REVIEW EXERCISES>Q 6

The difference between the simple interest and the compound interest on a certain sum for

2

years at the rate of

10 %

is

₹ 50

. Find the principal.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>REVIEW EXERCISES>Q 7

In how many years will a sum of

₹ 30, 000

amount to

₹ 31, 827

at the rate of

6 %

per annum compounded semi-annually?

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>REVIEW EXERCISES>Q 8

A library had

8, 000

registered members. The membership increased at the rate of

5 %

every six months. After what time will the total membership be

9, 261

?

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>THINKING SKILLS>Q 1

A sum of money amounts to $₹ 1, 210$ in $2$ years and to $₹ 1, 610.51$ in $5$ years. Find the principal and the rate of interest when interest is compounded annually.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>THINKING SKILLS>Q 2

A sum of money amounts to

₹ 8820

in

1

year and to

₹ 9, 261

in

1 \frac{1}{2}

years when interest is compounded semi-annually. Find the sum and the rate of interest per annum.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>THINKING SKILLS>Q 3

A farmer borrowed $₹ 12, 800$ from a moneylender to install a jet pump. The rate of interest is $11 \frac{1}{4} %$ per annum compounded annually. At the end of $2$ years, the farmer cleared the loan by paying $₹ 10, 842$ and a gold ring. Find the cost of the ring.

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>VALUES AND LIFE SKILLS>Q 1

Gita borrowed

₹ 2, 500

from a finance company for

1 \frac{1}{2}

years at the rate of

16 %

per annum. What amount will she have to pay if the interest is compounded half-yearly? Why should we always pay our loan on time?

MEDIUM

8th CBSE

IMPORTANT

START UP MATHEMATICS>Chapter 13 - Compound Interest>VALUES AND LIFE SKILLS>Q 2

Sahil invested $₹ 40, 000$ in a certain policy at the compound interest of $5 %$ per annum. After a certain period of time, he received $₹ 44, 100$ . Find the period of time for which the amount was invested. Give one point which you think one should keep in mind while investing in policies.