# FV, FVA, PV, PVA

I am learning about simple time value of money equations and I was wondering

1. If I see interest rate or inflation rate, can I use this value as the rate variable in all formulas?

2. Can all the FV, FVA, PV, PVA questions undergo compounding?

Ex. How much would you have in savings if you kept \$200 on deposit for 8 years @ 8%, compounded semiannually?

• Pay attention to the compounding period, it makes a difference. Commented Oct 28, 2017 at 5:04

Discount rates, which are what you use to find the present value, are a distinct concept from interest rates. The latter has several meanings but generally refers to how much you would earn on a particular account or investment. As we look for discount rates, an appropriate rate for discounting would be a fair interest rate being paid on an investment of similar risk. For that reason it is common in problems in school to see interest rates presented as a way for you to know what rate to use for discounting. But many interest rates and certainly inflation are inappropriate for discounting. For a given cash flow, there is a discount rate appropriate to its risk, which may also be an interest rate on a similar investment.

The second part of your question doesn't make a ton of sense as it is now so I'll just try my best to clear things up.

"Compounding" is a word used in the context of interest being paid. The mathematics of discounting can be set up to look like semi-annual or annual compounding, or it can be continuous compounding. They all give the same answer if you use an appropriate rate and accompanying math. For a given starting value and ending value, there is a continuously compounded rate, an annual rate, a semi-annual rate, and every other conceivable frequency. They all give the same answer at all horizons. Bottom line, don't get caught up on the concept of compounding unless your investment really has the property that if you withdraw early you don't get a partial interest payment.

OK, how do we interpret "8% semi-annually compounded?" Those words really should not be used together, but it is common in practice to use this language. What this generally means is 4% every 6 months. The equivalent annual rate is (1.04)^2 -1 = 8.16%. The equivalent continuous rate is 2*ln(1.04) = 7.84%. All these rates give the same answer if used with the right math.

200*(1.04)^16 = 374.60

200*(1.0816)^8 = 374.60

200*exp(8*0.0784) = 374.60

• The only reason compounding is confusing is that historically bankers have been lazy to calculate roots and divided instead (conveniently making themselves more money in the process) Commented Oct 28, 2017 at 11:59