IB Mathematics Analysis and Approaches Topic SL 1.4—financial Apps – Compound Interest, Annual Depreciation Revision Notes (SL/HL) | RevisionDojo

Financial Applications: Compound Interest and Annual Depreciation

Compound Interest

Simple interest is interest that provides a fixed amount each period, for example, 5% of the original amount you put in.
Compound interest, meanwhile, increases each period by a percentage of the current amount.
This doesn't sound like a big difference, but exponential growth is a powerful thing, and a bank account with compound interest can end up significantly richer than one with simple interest.

Example

Let's deposit $\text{\$}5000$ into two accounts, both with 5% annual interest.
Account $A$ has simple interest, and account $B$ has compound interest.
Account A's balance increases every year by $\text{\$}(0.05\times5000)=\text{\$}250$.
Meanwhile, account B's balance gets multiplied by $1.05$ every year.
After 50 years, account A will have a balance of $$\text{\$}(5000+50(0.05\times5000))=\text{\$}17500$$
After 50 years, account B will have a balance of $$\text{\$}5000(1.05)^{50}\approx \text{\$}57337$$
You can see here how compound interest is a lot more profitable than simple interest!

The Basic Formula

The compound interest formula is: $$ A = P(1 + r)^n $$ where:

$A$ is final amount
$P$ is principal (initial investment)
$r$ is interest rate (as a decimal)
$n$ is number of compounding periods

Tip

When converting interest rates to decimals, divide the percentage by 100.
For example, 5% becomes 0.05

This might look familiar.

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Definition

Paywall

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Note

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Tip

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Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

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Financial Applications: Compound Interest and Annual Depreciation

Compound Interest

Simple interest is interest that provides a fixed amount each period, for example, 5% of the original amount you put in.
Compound interest, meanwhile, increases each period by a percentage of the current amount.
This doesn't sound like a big difference, but exponential growth is a powerful thing, and a bank account with compound interest can end up significantly richer than one with simple interest.

Example

Let's deposit $\text{\$}5000$ into two accounts, both with 5% annual interest.
Account $A$ has simple interest, and account $B$ has compound interest.
Account A's balance increases every year by $\text{\$}(0.05\times5000)=\text{\$}250$.
Meanwhile, account B's balance gets multiplied by $1.05$ every year.
After 50 years, account A will have a balance of $$\text{\$}(5000+50(0.05\times5000))=\text{\$}17500$$
After 50 years, account B will have a balance of $$\text{\$}5000(1.05)^{50}\approx \text{\$}57337$$
You can see here how compound interest is a lot more profitable than simple interest!

The Basic Formula

The compound interest formula is: $$ A = P(1 + r)^n $$ where:

$A$ is final amount
$P$ is principal (initial investment)
$r$ is interest rate (as a decimal)
$n$ is number of compounding periods

Tip

When converting interest rates to decimals, divide the percentage by 100.
For example, 5% becomes 0.05

This might look familiar.

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics

IB Mathematics Analysis and Approaches SL 1.4—financial Apps – Compound Interest, Annual Depreciation Notes

Financial Applications: Compound Interest and Annual Depreciation

Compound Interest

The Basic Formula

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Duis aute irure dolor in reprehenderit

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Financial Applications: Compound Interest and Annual Depreciation

Compound Interest

The Basic Formula

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Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics