Compound interest

Algebra Level 1

Sidney has $10 in a savings account that earns 10% interest, compounded annually.

To the nearest cent, how much money will she have in 1 year?

Hint: Use the formula $B = p(1 + r)^t$ , where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

$13 $11 $12

1 solution

Michael Mendrin
Sep 20, 2016

Wrong formula:

$B=p\left(1+r\right)t=10\left(1+0.1\right)1=11$

Correct formula (see Zee Ell):

$B=p{\left(1+r\right)}^{t}=10{\left(1+0.1\right)}^{1}=11$

The formula for calculating compounded interest is

$B = p × (1 + r)^t$

instead of

B = p(1 + r)t

While compounding does not make a difference when t = 1 (as it is in this case), it has a significant effect when we have many compounding periods (t) and/or a large principal.

Zee Ell - 4 years, 8 months ago

Yeah, that's right, it should be the to the $t$ th power. But I used the formula as-is. After all, it's accurate for $t=1$ year

Michael Mendrin - 4 years, 8 months ago

Yes, I see that you've used the formula given at the question. It is still not right, so I also reported it earlier. Hopefully, it will be corrected some time later.

In the meantime, it would be great if you could make an adjustment to your solution (use the correct formula).

Zee Ell - 4 years, 8 months ago

@Zee Ell – Oh ALL right

Michael Mendrin - 4 years, 8 months ago

Compound interest

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