Answer:
3 years
Explanation:
The computation of the time period is shown below
Present value of annuity = Annuity × [1 - (1 + interest rate)^-time period] ÷ rate
$2,000 = $734.42 × [1 - (1.05)^-n] ÷ 0.05
$2,000 = $14,688.4 × [1-(1.05)^-n]
1-(1.05)^-n = ($2000 ÷ $14,688.4)
(1.05)^-n = 1 - ($2000 ÷ $14,688.4)
( 1 ÷ 1.05)^n = 0.86383813
Now take the log to the both sides
n × log(1 ÷ 1.05) = log0.86383813
n = log0.86383813 ÷ log (1 ÷ 1.05)
= 3 years
