Rich deposited money into a bank account that earned 2.5% simple interest each year. After 2 years, he had earned $14.65 in interest on the account. If no other money was deposited into or withdrawn from the account, how much was his initial deposit?
The formula for simple interest is
\(I=Prt\)
where I=interest earned, P=initial deposit, r=rate of increase, and t=time.
We have
\(I=14.65\)
\(r=2.5\%=0.025\)
\(t=2\)
Plug in:
\(14.65=P(0.025)(2)\)
Solve for \(P\):
\(14.65=0.05P\)
\(\rightarrow P=293\)
So the initial deposit was $293.