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You put $1000 into a savings account yielding 6% annual interest; you left the money in for two years. How much interest do you get at the end of those two years?

1 Answer

Nov 9, 2016

Assuming annual compounding:
$XXX $ 1123.60$ $color(white)("XXX")color(green)($1123.60)$

Explanation:

Each year the investment would increase by $6 %$ $6%$
or stated anther way, each year the investment would become $1.06$ $1.06$ times what it had been.

With an initial investment of $$ 1000$ $$1000$
after $1$ $1$ year, the investment would be worth $$ 1000 \times 1.06$ $$1000 xx 1.06$
after $2$ $2$ years, the investment would be worth $($ 1000 \times 1.06) \times 1.06$ $($1000xx 1.06) xx 1.06$

In general, after $n$ $n$ years the investment would be worth:
$XXX $ 1000 \times {(1.06)}^{n}$ $color(white)("XXX")$1000xx(1.06)^n$

For the specific case of $2$ $2$ years
$XXX $ 1000 \times {(1.06)}^{2} = $ 1123.60$ $color(white)("XXX")$1000xx(1.06)^2=$1123.60$

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