An annuity that pays $12,500 a year at an annual interest rate of 5.45 percent costs $150,000 today. What is the length of the annuity time period

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:-

$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:

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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

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