Time Value of Money
tvm computes one of the future value, present value, payment, or number of periods given the interest rate and given the remaining values.
For example, consider case where you have a interest bearing account that pays 5% per annum compounded monthly. If you start with $10,000, you can compute the amount you will have after 10 years with:
tvm --pv=10000 --rate=5 --freq=12 --years=5 fv
The value in 5 years is referred to as the future value (fv). The current amount is the present value (pv). The frequency is the number of periods per year. The program responds with:
fv = $12,833.59 pv = $10,000.00 pmt = $0.00 r = 5% N = 60
You can specify values with SI scale factors, units, and commas. So you can do the same thing with either:
tvm --pv='$10,000' --rate=5% --freq=12 --years=5 fv
tvm --pv=10k --rate=5% --freq=12 --years=5 fv
The quotes are needed in the first case to prevent $ from being interpreted by the shell.
tvm remembers the values specified on the previous invocation and uses them if they are not specified. This allows you to rapidly run what-if experiments without having to re-specify values that do not change. So, once you have run the first command, you can now quickly determine how much you will have in 10 years using:
tvm -y 10 fv = $16,470.09 pv = $10,000.00 pmt = $0.00 r = 5% N = 120
Without changing anything else, you can determine what happens if you make an additional $100 contribution each month:
tvm --pmt 100 fv = $31,998.32 pv = $10,000.00 pmt = $100.00 r = 5% N = 120
You can also use tvm to explore loans. For example, you can compute the payment for a mortgage given the principal and interest rate:
tvm --ignore --pv=-250k --rate=4.375 --years=30 pmt pmt = $1,248.21 pv = -$250,000.00 fv = $0.00 r = 4.38% N = 360
The –ignore option was added so that we start from scratch; any values that were previously specified are ignored.
You can now understand how paying a little extra affects how long it takes to pay off the loan:
tvm --pmt=1.5k years years = 21.42 pv = -$250,000.00 pmt = $1,500.00 fv = $0.00 r = 4.38% N = 257.08
pip3 install --user tvm
This installs tvm to ~/.local/bin; make sure this directory is on your path.
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