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

Answer

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Answer

$P V = 105, 156.79$

Steps

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

Step 2 ： $n = 9 \times 12 = 108$

Step 3 ： $P V = P M T \times [\frac{1 - (1 + r)^{- n}}{r}]$

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

Step 5 ： $P V = 1531 \times [\frac{1 - {1.00916667}^{- 108}}{0.00916667}]$

Step 6 ： $P V = 1531 \times [\frac{1 - 0.370391}{0.00916667}]$

Step 7 ： $P V = 1531 \times [\frac{0.629609}{0.00916667}]$

Step 8 ： $P V = 1531 \times 68.6826$

Step 9 ： $P V = 105, 156.79$