Question

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The amount of money, A(t), in a savings account that pays 5% interest, compounded quarterly for t years,
when an initial investment of $1600 is made, is given by
A(t)=1600(1.0125) ^4t
Find A(5) - A(1)/5-1=

Interpret the result

Answer 1

A(t) = 1600(1.0125)^(4t)

A(1) = 1600(1.0125)^(4*1)

A(1) = 1681.5125390625

A(1) = 1681.51

After 1 year, you'll have $1681.51 in the account.

A(t) = 1600(1.0125)^(4t)

A(5) = 1600(1.0125)^(4*5)

A(5) = 2051.25957073373

A(5) = 2051.26

After 5 years, you'll have $2051.26 in the account.

Then,

`(A(5)-A(1))/(5-1)=(2051.26-1681.51)/(5-1)\\\\(A(5)-A(1))/(5-1)=(369.75)/(4)\\\\(A(5)-A(1))/(5-1)=92.4375\\\\(A(5)-A(1))/(5-1)=92.44\\\\`

Interpretation: you earn about $92.44 per year over the period from year 1 to year 5.

This is the average rate of change (aka slope). The A(5)-A(1) in the numerator represents the "rise", and the "5-1" in the denominator is the "run".