What cash payment is equivalent to making payments of $\$ 1531.00$ at the end of every month for 9 years if interest is $11 \%$ per annum compounded quarterly?
The cash payment is $\$ \square$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer

Expert–verified

Hide Steps

Answer

$ \boxed{PV = 105,156.79} $

Steps

Step 1 ：$ r = \frac{11\%}{4} \div 3 = 0.916667\% $

Step 2 ：$ n = 9 \times 12 = 108 $

Step 3 ：$ PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right] $

Step 4 ：$ PV = 1531 \times \left[\frac{1 - (1 + 0.00916667)^{-108}}{0.00916667}\right] $

Step 5 ：$ PV = 1531 \times \left[\frac{1 - 1.00916667^{-108}}{0.00916667}\right] $

Step 6 ：$ PV = 1531 \times \left[\frac{1 - 0.370391}{0.00916667}\right] $

Step 7 ：$ PV = 1531 \times \left[\frac{0.629609}{0.00916667}\right] $

Step 8 ：$ PV = 1531 \times 68.6826 $

Step 9 ：$ \boxed{PV = 105,156.79} $