Respuesta :
Answer:
20 years
Explanation:
The computation of the length of the annuity time period is shown below:-
Present value of annuity=Annuity[1-(1+interest rate)^-time period] ÷ rate
$150,000 = $12,500 × (1 - (1.0545)^-time period) ÷ 0.0545
$150,000 = 229,357.7982 × (1-(1.0545)^-time period)
(1-(1.0545)^-time period) = (150,000 ÷ 229,357.7982)
1 - (150,000 ÷ 229,357.7982) = (1.0545)^-time period
(1.0545)^-time period = 0.346
(1 ÷ 1.0545)^time period = 0.346
now we will take log on both sides:
time period*log(1/1.0545)=log 0.346
time period=log 0.346/log(1 ÷ 1.0545)
= 20 years
An annuity is a term that is referred to as the agreement or the long-term contract that accumulates the funds in the form of a guaranteed income. Many of the people get distracted from the purchase of the annuity analyzing their simplicity and there's a mistake they do.
The computation of the length of the annuity time period is shown below:-
[tex]\begin{aligned}\text{Present value of annuity}=\frac{Annuity[1-(1+\text{interest rate})^-\text{time period}}{rate}\end{aligned}[/tex]
$150,000 = $12,500 × (1 - (1.0545)^-time period) ÷ 0.0545
$150,000 = 229,357.7982 × (1-(1.0545)^-time period)
(1-(1.0545)^-time period) = (150,000 ÷ 229,357.7982)
1 - (150,000 ÷ 229,357.7982) = (1.0545)^-time period
(1.0545)^-time period = 0.346
(1 ÷ 1.0545)^time period = 0.346
Now we will take log on both sides:
time period*log(1/1.0545)=log 0.346
time period=log 0.346/log(1 ÷ 1.0545) = 20 years
Therefore, the length of the annuity time period is 20 years.
To know more about the annuity period, refer to the link below:
https://brainly.com/question/4579968
