# Should I pay for the whole year first or pay in monthly installments?

I have two options for getting a new internet connection.

• Option A - Pay 2500 for the router and then pay 500 at the end of every month for the next twelve months.
• Option B - Pay 6000 for both the router and the internet connection for the next twelve months. No other charges.

How can I use time value of money to find the present value of money if I choose to go with option A?

Assume that my discount rate is 12%. Can I just divide by twelve to get the monthly interest rate? It seems like to get an accurate answer the calculation of the interest rate should take into account compounding period as well?

The short answer is you'd be much better off paying up front in this case. The present value of \$2,500 plus 12 \$500 monthly payments is \$8,128 at a 12% discount rate, which is much higher then the \$6,000 you could pay now.

The long answer is how you get that present value.

How can I use time value of money to find the present value of money if I choose to go with option A?

First of all, I'd question your discount rate. A 12% discount rate means that you can safely reinvest the money that you're not spending today at a 12% annual (1% monthly) rate, which seems very high. Normally for short-term spending decisions you'd use a risk-free rate, which would be closer to 1%-2%. However, to discount at 1% monthly you'd just divide each monthly payment by 1 plus the discount rate raised to the power of the number of periods until each payment. So the total is

``````            \$50         \$50               \$50
\$2,500 + --------  + --------  + ... + ---------
(1.01)^1    (1.01)^2          (1.01)^12
``````

which is `\$8,127.54`

You could also use the `NPV` function in Excel.

It seems like to get an accurate answer the calculation of the interest rate should take into account compounding period as well?

Correct, and in the example above the compounding is assumed to be monthly since that's the periodicity of the cash flows. You could calculate it with a different compounding period but it gets much more complicated and probably wouldn't make a significant difference.

The discount rate does take compounding into effect, meaning if you saved the \$5,628 (the PV of \$8,128 minus the \$2,500 initial payment), you'd earn 1% interest on \$5,628 the first month, \$5,128 plus that interest the second month, etc.