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

5. Homework Pg. 401 #1, 3, 5