Question

write a function of $5000 deposit that earns 7.2% annual interest compounded monthly that represents the balance after t years.

Answer 1

The compounding interest formula is :

`A=P(1+(r)/(n))^(nt)`

where A = future amount after t years

P = Initial amount

r = rate of interest

n = number of compounding

From the problem :

P = 5000

r = 7.2% or 0.072

n = 12 (compounded monthly)

Using the formula above :

`\begin{gathered} A=5000(1+(0.072)/(12))^(12t) \\ A=5000(1.006)^(12t) \end{gathered}`

The function will be :

`A(t)=5000(1.006)^(12t)`

Additional Information :

The formula was derived from :

`A=P+I`

where P = principal amoutn

A = future amount

I = Interest

The formula for interest is :

`I=P((r)/(n))`

Substitute it to the formula above :

`\begin{gathered} A=P+I \\ A=P+P((r)/(n)) \end{gathered}`

Factor out P :

`A=P(1+(r)/(n))`