Find the compound interest on rs. 12500 at 8% per annum for 9 months compounded quarterly.

The sooner you start to save, the more you'll earn with compound interest.

How compound interest works

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.

This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.

Save more with compound interest

The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.

For example, if you put $10,000 into a savings account with 3% interest compounded monthly:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r)n

A = ending balance
P = starting balance (or principal)
r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods

How to calculate compound interest

To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:

1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042

2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24

3. Use the compound interest formula

A = $2,000 x (1+ 0.0042)24
A = $2,000 x 1.106
A = $2,211.64

Lorenzo and Sophia compare the compounding effect

Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.

After five years:

• Sophia has $12,834.
• Lorenzo has $12,500.

Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.

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Jump to

• Compound Interest Exercise 2.1
• Compound Interest Exercise 2.2
• Compound Interest Exercise 2.3

• Rational and Irrational Numbers
• Compound Interest
• Expansions
• Factorization
• Simultaneous Linear Equations
• Problems on Simultaneous Linear Equations
• Quadratic Equations
• Indices
• Logarithms
• Triangles
• Mid Point Theorem
• Pythagoras Theorem
• Rectilinear Figures
• Theorems on Area
• Circle
• Mensuration
• Trigonometric Ratios
• Trigonometric Ratios and Standard Angles
• Coordinate Geometry
• Statistics

ML Aggarwal Solutions Class 9 Mathematics Solutions for Compound Interest Exercise 2.2 in Chapter 2 - Compound Interest

Question 24 Compound Interest Exercise 2.2

(i) In what time will ₹ 1500 yield ₹ 496.50 as compound interest at 10% per annum compounded

annually?

(ii) Find the time (in years) in which ₹ 12500 will produce 3246.40 as compound interest at 8% per annum,

interest compounded annually.

Answer:

(i) It is given that

Principal (P) = ₹ 1500

CI = ₹ 496.50

So the amount (A) = P + SI

Substituting the values

= 1500 + 496.50

= ₹ 1996.50

Rate (r) = 10% p.a.

We know that

Here Time n = 3 years

(ii) It is given that

Principal (P) = ₹ 12500

CI = ₹ 3246.40

So the amount (A) = P + CI

Substituting the values

= 12500 + 3246.40

= ₹ 15746.40

Rate (r) = 8% p.a.

We know that

By further calculation

Here Period = 3 years

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