5F Compound Interest, 5G Depreciation Unit 8: Number and algebra 5F, 5G 5/20/2019 4:35 PM

Compound Interest after a certain amount of time (period) the bank adds money to the account (interest) which is a percentage of the money (rate) “compound” because interest generated in one period will itself earn interest in the next period deposit: 6000 USD annual interest rate: 8% term: 3 years period: yearly Year Principal (USD) Interest (USD) Balance (USD) 1 6000.00 6000.00(0.08) = 480.00 6480.00 Year Principal (USD) Interest (USD) Balance (USD) 1 6000.00 6000.00(0.08) = 480.00 6480.00 2 6480.00(0.08) = 518.40 6998.40 3 6998.40(0.08) = 559.87 7558.27 Year Principal (USD) Interest (USD) Balance (USD) 1 6000.00 6000.00(0.08) = 480.00 6480.00 2 6480.00(0.08) = 518.40 6998.40 5F, 5G 5/20/2019 4:35 PM

Formula Copy FV : future value PV : present value n : number of years r% : nominal annual interest rate k : number of compounding periods per year k = 1 yearly k = 2 half-yearly k = 4 quarterly k = 12 monthly interest earned: 5F, 5G 5/20/2019 4:35 PM

Examples 5F, 5G 5/20/2019 4:35 PM

GDC’s TVM Solver (“Apps”, then “Finance”) Copy Time Value of Money (FOR INVESTMENTS) N : TOTAL number of years I% : nominal annual interest rate (should be positive) PV : present value (investments are negative) PMT : payment each time period (MUST BE zero) FV : future value (should be positive) P/Y : payments per year (MUST BE one) C/Y : compound periods per year PMT END BEGIN : payments during period (choose end) Enter in all but one of the values and then highlight the value you want to find. Press ALPHA and then SOLVE (ENTER). DO NOT USE THE TVM SOLVER METHOD AS EXPLAINED BY THE TEXTBOOK (IT WORKS BUT IN A DIFFERENT WAY THAT WILL MAKE IT CONFUSING IN THE LONG RUN) 5F, 5G 5/20/2019 4:35 PM

5F Compound Interest, 5G Depreciation Examples when using TVM Solver, write down all of the values you see on the TVM Solver screen to show your work (the one time it’s appropriate to use “calculator speak”) 5F, 5G 5/20/2019 4:35 PM

5F, 5G 5/20/2019 4:35 PM

Depreciation loss in value of an item over time value: 8500 USD depreciation rate: 30% After the first year, what percentage of the original value is the book value? Exponential growth or decay? What are the possible book values? Year Depreciation (USD) Book Value (USD) 8500.00 1 8500(0.30) = 2550.00 5950.00 Year Depreciation (USD) Book Value (USD) 8500.00 Year Depreciation (USD) Book Value (USD) 8500.00 1 8500(0.30) = 2550.00 5950.00 2 5950.00(0.30) = 1785.00 4165.00 3 4165.00(0.30) = 1249.50 2915.50 Year Depreciation (USD) Book Value (USD) 8500.00 1 8500(0.30) = 2550.00 5950.00 2 5950.00(0.30) = 1785.00 4165.00 5F, 5G 5/20/2019 4:35 PM

Depreciation Formula (not in formula booklet) Copy FV : future value PV : present value n : number of years r% : nominal depreciation rate per year (must be negative) k : always one since the depreciation rate is annual value lost: we tend to (for depreciation) just use TVM Solver but make sure the nominal rate is negative 5F, 5G 5/20/2019 4:35 PM

GDC’s TVM Solver (“Apps”, then “Finance”) Copy Time Value of Money (FOR DEPRECIATION) N : TOTAL number of years I% : nominal annual depreciation rate (should be negative) PV : present value (negative) PMT : payment each time period (zero) FV : future value (positive) P/Y : payments per year (enter “1”) C/Y : periods per year (enter “1”) PMT END BEGIN : payments during period (choose end) Enter in all but one of the values and then highlight the value you want to find. Press ALPHA and then SOLVE (ENTER). 5F, 5G 5/20/2019 4:35 PM

Examples 5F, 5G 5/20/2019 4:35 PM

5F Compound Interest, 5G Depreciation Guided Practice p. 148: 1 p. 153: 3,5 Use TVM Solver Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers. Copy 5F, 5G 5/20/2019 4:35 PM