Set up a time-value-of-money calculation

Setting up TVM fields

A TVM setup records the starting value, regular cash flow and ending value in standard fields. The period count, frequency fields and signs must describe the same model and viewpoint

1. Map each field to its time Use PV for the starting amount, PMT for the regular cash flow and FV for the balance after all listed periods \(\displaystyle PV=V_0,\quad PMT=D,\quad FV=V_N\)
2. Count all payment periods Convert years to the total number of payments using the frequency per year \(\displaystyle N=4\times3=12\)
3. Match both frequency fields For this model, payments per year and compounding periods per year use the same frequency \(\displaystyle P/Y=C/Y=4\)
4. Use opposite cash-flow signs Choose one viewpoint and give money received and money paid opposite signs \(\displaystyle PV=-\$2{,}500,\quad PMT=-\$120,\quad FV=+F\)

Worked example

Set up the TVM fields for a savings account with $2,500 at the start, 6% p.a. compounded monthly, and $120 deposited at the end of each month for 2 years. Use the customer's viewpoint and leave FV as the unknown

1. \(\displaystyle N=12\times2=24,\quad P/Y=C/Y=12\)Two years of monthly payments gives 24 payments, with 12 payments and compounding periods per year
2. \(\displaystyle I/Y=6\%\)Enter the nominal annual rate as the rate quoted for the account
3. \(\displaystyle PV=-\$2{,}500,\quad PMT=-\$120\)From the customer's viewpoint, the starting amount and deposits are money paid into the account
4. \(\displaystyle FV=?\)The balance after all 24 deposits is the unknown future value

Common mistakes

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