Answer:
The value of annuity is [tex]P_v = \$ 32058[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 1500[/tex]
The interest rate is [tex]r = 8\% = 0.08[/tex]
Frequency at which it occurs in a year is n = 2 (semi-annually )
The number of years is [tex]t = 22 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)
substituting values
[tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]
[tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]
[tex]P_v = \$ 32058[/tex]
