Suppose you invest $8500 in an account
that earns seven percent simple interest annually.
Use this information to complete the table below.
Round to the nearest cent as needed.
Notice how the first row is given for us where the starting
balance is $8500, the simple interest for the first year
is $595 and the ending balance is $9095
which is the sum of 8500 and 595.
Because this account earns simple interest annually,
this interest amount is not going to change over the five
years, it will be $595 each year because for simple
interest, the interest is based upon the starting balance
not the increasing balance over time.
Let's go ahead and check to make sure the $595
is correct by using the simple interest formula I equals
P sub zero times R times T where I is the interest amount
in dollars, P sub zero is the beginning balance in dollars,
R is the annual interest rate as a decimal, and T is time
in years.
So if we use I equals P sub zero times R times T
we have I the interest is equal to 8500 times the rate
as a decimal which is 0.07 times the time in years
which is one.
Let's just make sure this product is $595.
We have 8500 times .07 times one,
which does give us the amount of simple interest of $595.
And of course we can sum these two amounts to check 9095,
but let's also use the second simple interest formula
here where A is the balance in dollars after two years
and P sub zero is the starting balance, R is the annual
simple interest rate as a decimal and T is time in years.
Applying this formula, we should get $9095 but let's
just check.
We have A equals 8500 times the quantity one plus R
as a decimal is 0.07 times T in years and therefore T is one
and now let's evaluate this on the calculator.
We have 8500 and then in parentheses one plus 0.07
times one the times one isn't needed, Enter.
And notice how we do get 9095.
And now to complete the table, the ending balance
for year two is going to be $9095 plus the interest
of $595 which gives us $9690.
The ending balance for year two is the beginning balance
for year three and again the interest is still $595
and therefore the ending balance which is given to us
is $9690 plus $595 which is $10285.
The ending balance in year three is the beginning balance
in year four and then we take the beginning balance
of year four, add the interest of $595 to get
the ending balance in year four, $10285 plus $595
is $10880.
The ending balance in year four is the beginning balance
in year five.
And again to find the ending balance in year five,
we take the beginning balance, add the interest,
$10880 plus $595 is $11475.
I hope you found this helpful.