Suppose you borrow $4,000
at an 18% annual interest rate compounded monthly,
which comes out to an interest rate of 1.5% each month.
At the end of each month, you make a $150 payment.
Use this information to complete the table below.
Round to the nearest cent as needed.
Looking at the table, we will say the ending balance
at the end of month zero, which is right
when you receive the money, is $4,000,
which becomes the prior balance at the beginning
of month one.
Then during month one, you are charged 1.5% interest
on the balance of $4,000.
Which means now we need to find 1.5% of 4,000.
To do this, we convert 1.5% to a decimal
and multiply it by 4,000.
1.5% is equal to 0.015 as a decimal.
Then we have times 4,000,
which is equal to 60.
Which means you're charged $60 of interest
during month one.
And then you make the payment of $150,
and now to determine the ending balance,
we take the prior balance, add the interest,
and then subtract the payment.
4,000 plus 60 minus 150 is 3,910,
giving an ending balance at the end of month one of $3,910.
Notice how the balance only decreased by $90
because of the 150, 60 paid off the interest
and only 90 decreased the balance.
And now the prior balance for month two is $3,910.
And now during month two,
you're charged 1.5% interest on $3,910.
So let's use the calculator and determine 1.5% of 3,910.
We convert 1.5% to a decimal, which is 0.015,
and then we have times 3,910.
The interest during month two is $58.65.
And then you make a payment of $150,
and therefore the ending balance at the end of month two
is 3,910 plus 58.65
minus the payment of 150,
which is equal to $3,818.65.
This becomes the prior balance
at the beginning of month three.
And now during month three, you are charged
1.5% interest on the balance of $3,818.65.
Going back to the calculator,
0.015 times 3,818.65.
Rounding to the nearest cent, we have $57.28
of interest during month three.
And then you make the payment of $150,
and therefore the ending balance for month three
is $3,818.65 plus 57.28 minus 150,
which is equal to $3,725.93.
This becomes the prior balance for month four.
And then you're charged 1.5% interest
on this balance.
Going back to the calculator,
to the nearest cent, you are charged $55.89 of interest
during month four.
Then you make the payment of $150.
The ending balance for month four is 3,725.93
plus 55.89 minus 150,
which is $3,631.82.
And this becomes the prior balance for month five.
Then during the fifth month, you are charged 1.5%
interest on this balance.
Which to the nearest cent is $54.48.
The ending balance for month five is 3,631.82
plus 54.48 minus 150,
which is equal to $3,536.30.
Notice during these five months,
less than $100 is used to reduce the balance of the account,
and more than $50 is used just to pay off the interest.
I hope you found this helpful.