Answer:
The present value is $21070.31
Step-by-step explanation:
Given: semi-annual payments of $2,527 at 6.1% compounded semi-annually over a 6 year period.
We have to find the present value given that semi-annual payments of $2,527 at 6.1% compounded semi-annually over a 6 year period.
Given that payment is made semi annually that is 2 times in a year.
Given Payment made = $2527.
Rate of interest =6.1% compounded semi annually = 0.061
Time period = 6 years = 6 × 2 = 12
Thus, [tex]P=\dfrac{A\cdot i}{1-(1+i)^{-t}}[/tex]
Where A denotes the amount to pay
P is payment made
t is time period
i is interest rate
Substitute the values, we get,
[tex]2527=\dfrac{A\cdot(0.061) }{1-(1+0.061)^{-12}}[/tex]
Cross multiply and Solve for A, we get,
[tex]A=2527\cdot\frac{\left(1-\left(1+0.061\right)^{-12}\right)}{0.061}[/tex]
A=21070.306476
Thus, the present value is $21070.31
