Finance: Compound interest

Finance: Compound interest

Now that we understand the concepts behind exponential growth and decay, let's utilize them and solve real-life problems! One of the many areas where exponential growth comes in handy is Finance. In this section, we will learn how compound interest helps us grow our deposits in our investment and/or bank accounts.
Basic concepts: Order of operations with exponents, Using exponents to solve problems,
Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

Lessons

exponential growth/decay: Af=Ai(1+rn)nt { A_f = A_i (1+\frac{r}{n})^{nt}}

Af {A_f} : final amount
Ai {A_i} : initial amount
r {r} : Annual interest rate
t {t} : total time given in years
n {n} : number of times compounded in a year, if

Compound daily:

n = 365

Compound monthly:

n = 12

Compound quarterly:

n = 4

Compound semi-annually:

n = 2

Compound annually:

n = 1

  • 1.
    Bianca deposits $1,000 in a savings account with an annual interest rate of
    12%. How much money will she have in 20 years, if the interest is compounded:
    a)
    daily

    b)
    monthly

    c)
    quarterly

    d)
    semi-annually

    e)
    annually

  • 2.
    A $1000 investment, compounded quarterly, doubles in value over a period
    of 8 years. Find the interest rate per annum.
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21.
Applications of Exponential Functions
21.1
Exponential growth and decay by a factor
21.2
Exponential decay: Half-life
21.3
Exponential growth and decay by percentage
21.4
Finance: Compound interest
21.5
Continuous growth and decay
AU Maths Methods
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