Question

The principal represents an amount of money deposited in a savings account subject to

compound interest at the given rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
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A. The amount of money in the account after 5 years is $
(Round to the nearest hundredth as needed.)
Principal
$11,000
Rate
5%
Compounded
annually
Time
5 years

Answer 1

Explanation:

So the general formula for compound interest is
`A = P(1+(r)/(n))^(nt)` where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just
`A = P(1+r)^t`. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula
`A = 11000(1.05)^t`. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be
`11000(1.05)^t-11000`. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation
`11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10`