Question

A $100 annual annuity for 20 years is worth $1,650 today. What is the interest rate?

Answer 1

The interest rate is computed as follows:

Present value = Annual annuity x [ (1 – 1 / (1 + r)ⁿ) / r ]

$ 1,650 = $ 100 x [ (1 - 1 / (1 + r)²⁰ ) / r ]

16.5 = [ (1 - 1 / (1 + r)²⁰ ) / r ]

To match the above equation, we shall plug in r as 1.91% as shown below:

16.5 = [ (1 - 1 / (1 + 0.0191)²⁰ ) / 0.0191 ]

16.5 = 16.5 Approximately

Hence the interest rate is 1.91% Approximately

We can also compute the rate by using excel as follows:

= RATE(N,PMT,PV,FV)

= RATE(20,100,-1650,0)

It will also give interest rate equal to 1.91%

Do ask in case of any doubts.