Answered

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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

Sagot :

Answer:

$25

Explanation:

The compound interest formula gives

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

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.

[tex]A-P[/tex][tex]=P(1+\frac{r}{n})^{nt}-P[/tex]

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

[tex]2500(1+\frac{0.01}{1})^1-2500[/tex]

which simplifies to give

[tex]\begin{gathered} 2500(1+0.01)^{}-2500 \\ =\$25 \end{gathered}[/tex]

This tells us that the interest earned is $25.

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