Question

What’s the interest rate of a 5-year, annual $4,800 annuity with present value of $19,000?

Answer 1

PV of Annuity = P*[1-{(1+i)^-n}]/i

where. PV = 19000, P = Annuity = 4800, i = Interest Rate, n = Number of Periods = 5

19000 = 4800*[1-{(1+i)^-5}]/i

3.9583 = [1-{(1+i)^-5}]/i

By, Trial & Error method,

Taking i = 0.05, [1-{(1+i)^-5}]/i = [1-{(1+0.05)^-5}]/0.05 = 4.3295

Taking i = 0.07, [1-{(1+i)^-5}]/i = [1-{(1+0.07)^-5}]/0.07 = 4.1001

Taking i =0.08, [1-{(1+i)^-5}]/i = [1-{(1+0.08)^-5}]/0.08 = 3.9927

Taking i = 0.085, [1-{(1+i)^-5}]/i = [1-{(1+0.085)^-5}]/0.085 = 3.9406

Taking, i = 0.0833, [1-{(1+i)^-5}]/i = [1-{(1+0.0833)^-5}]/0.0833 = 3.9582

Therefore, Interest Rate = 0.0833 = 8.33%(approx)