Question

What is the interest earned in a savingsaccount after 12 months on a balance of$2500 if the interest rate is 1% APYcompounded yearly?Round your answer to the nearest hundredth

Answer 1

$25

Step-by-step explanation:

The compound interest formula gives

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

where

A = final balance

P = principle amount

r = interest rate /100

n = # of compounds applied per interval

t = # of intervals

The interest earned, therefore, is the difference of the final balance and principle.

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

Now in our case.

P = $2500

r = 1 / 100

n = 1 ( 1 year = 12 months )

t = 1 ( 12 months = 1 year )

Therefore, our formula gives

`2500(1+(0.01)/(1))^1-2500`

which simplifies to give

`\begin{gathered} 2500(1+0.01)^{}-2500 \\ =\$25 \end{gathered}`

This tells us that the interest earned is $25.