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

User Eleeist
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1 Answer

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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))

User Arian Motamedi
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