Question

Problem 5-34 Annuity Interest Rate (LG5-8) What's the interest rate of a 8-year, annual $3,500 annuity with present value of $20,000? (Use a time value of money calculator or a spreadsheet. Round your answer to 2 decimal places.) 010 Annuity interest rateſ

Answer 1

Present value of annutiy =$20000

Yearly annuity (P)= 3500

Number of annnuity (n) = 8

Present value of annuity = P*(1-(1/(1+i)^20))/i

We will calculate i by trial and error method.

Assume is is 8%

Present value of annutiy = 3500*(1-(1/(1+8%)^8))/8%

20113.2363

Assume i is 8.5%

Present value of annuity = 3500*(1-(1/(1+8.5%)^8))/8.5%

19737.14039

Actual value 20000 is in between above values. So we will calcuate rate of return (i) by trial and error method.

interpolation formula = lower i +( uper i - lower i)*(lower i value - Actual i value)/(lower i value- uper i value)

8%+( (8.5%-8%)*(20113.2363-20000)/(20113.2363-19737.14039))

=0.08150541786 or 8.15%

So annuity interest rate is 8.15%

Note : financial calculator or excel function = rate(number of periods, annuity, -Present value)

=rate(8, 3500, - 20000)

=8.15%

So exact rate of return implied is 6.75%

(please thumbs up)