Question

Hello, I am confused on the difference between PV and PV (annuity), FV and FV(annuity). I do not know when to use one formula over the other.

Is there a way you can simplify when to use each formula? The key differences? Key phrases or words I should associate them with? An easy way to remember how each formula is used? I am confused on TVM equations.

For example)

#1. You buy a property for $100,000 and you are offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment you must make? (Round to 2 decimal places)

#2. What is the present value (PV) of $200,000 received six years from now, assuming the interest rate is 8% per year?(Round to dollar)

I thought these questions used both PV formula, but the first question uses PV (annuity) and second one is just PV. Why is that? Do not need to solve the questions, just provide an explanation of how to use formulas and for what problems.. If you can make it as clear and easy to understand as possible, that would be appreciated.

Answer 1

When there is a single payment and you wish to find the Present Value or the Future Value, you should use the

Single Payment Present Worth Factor (P/F, i,N)=1/((1+i)^N)

i=Interest rate, N=Number of Years after which the Single Payment is made

Multiply this factor by the Single payment, You get the Present value (PV)

For Finding Future Value you use,

Single Payment Future Worth Factor (F/P, i,N)=(1+i)^N

i=Interest rate, N=Number of Years after which the Single Payment is made

Multiply this factor by the Single payment Now, You get the Future  value (FV)

When there are number of constant payments at constant intervals , it is called annuity.

To find the present value of number of fixed payment at constant interval , you use

Uniform Series Present Worth Factor(P/A,i,N)=(((1+i)^N)-1)/(i*((1+i)^N))

Multiply this factor by the constant periodic payment of A, you will get the Present Value (PV)

For Finding Future value of number of fixed periodic payments, you use,

Uniform Series Compound Amount Factor=(F/A, i,N)=(i*((1+i)^N))/(((1+i)^N)-1)

Multiply this factor by the fixed periodic payments of A, you will get the Future Value

In this Case#1

There are number of annual payments

i=Interest rate=8%=0.08, N=Number of payments=30

PV=$100,000=A*(((1+i)^N)-1)/(i*((1+i)^N))=A*(((1+0.08)^30)-1)/(0.08*((1+0.08)^30))=11.25778

A=PV/11.25778=100000/11.25778=$8882.74

Annual Payment of $8882.74 . Total payments=30

Case #2

There is a Single Payment =$200,000 at future after 6 years

i=8%=0.08

N=6

Present value =$200000*(1/((1+i)^N)=200000/((1+0.08)^6)=$126,033.93

Hope the Concepts are Clear>

If there are multiple payments , it is annuity

Otherwise, it is Single Payment