Payments and Total Interest

1
Payments and Total Interest
The two formulas used so far are only useful if
we know what the regular payment is going to be.
If we know what a future amount and want to find
out what regular payments we need to make in
order to accumulate to that amount, we rearrange
the previous formulas to solve for PMT.
Brainstorm situations where these formulas would
be useful.
2
Example 1 Sofia has a 12 000 student loan that
she must begin to repay. Payments are due at the
end of each month for the next 2 years, with
interest calculated at 9 per year, compounded
monthly. 1. Determine the amount of each
payment PMT ?? PV or FV 12 000 i 0.09
0.0075 12 n 2x12 24 2. Calculate
the total amount needed to repay the
loan. 548.22 x 12 x 2 13 157.28 3.
Calculate the total amount of interest that Sofia
will pay. 13 157.28 - 12 000 1157.28
3
Example 2 Cassandra has a little sister who is
going to need 40 000 for tuition in 9 years.
Her parents found an account that pays 4.7
interest compounded quarterly. 1. What regular
deposit must her parents make so that they will
have enough? PMT ?? PV or FV 40 000 i 0.047
0.01175 4 n 9 x 4 36 2.
Calculate the amount that her parent contributed
to the account over the 9 years. 899.05 x 4 x 9
32 365.80 3. Calculate the total amount of
interest they earned. 40 000 - 32 365.80
7634.20
4
Example 3 Gracie recently bought her first home
for 289, 000. Her mortgage broker found her a
mortgage for 5.1 compounded monthly, based on an
amortization period of 25 years. Amortization
period- the length of time for the mortgage to be
paid off. 1. Calculate the monthly mortgage
payment. PMT ?? PV or FV 289 000 i 0.051
0.00425 12 n 25x12 300 2.
Calculate the total paid for the house assuming
the payments remain the same for the duration of
the mortgage. 1706.35 x 12 x 25 511 905 3.
Calculate the total interest paid over the life
of the mortgage. 511 905 - 289 000 222 905
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Homework Pg. 401 1, 3, 5