Respuesta :
Answer:
They should deposit $105 every month so that they reach their goal.
Explanation:
Given - Liz and Bob just had a baby named Isabelle, and they want to
save enough money for Isabelle to go to college. Assume that
they start making monthly payments when Isabelle is 5 into an
ordinary annuity earning 3.79%, and they calculate that they will
need $21,200.00 by the time Isabelle turns 18.
To find - How much should they deposit every month so that they reach
their goal.
Proof -
We know the formula -
Future value = [tex]PMT\frac{(1 + i)^{n} - 1 }{i}[/tex]
Here , we have
i = [tex]\frac{\frac{3.79}{100} }{12} = \frac{{0.0379} }{12}[/tex]
n = 12×(18 - 5) = 156
Future value = 21,200.00
∴ we get
21,200.00 = [tex]PMT\frac{(1 + \frac{0.0379}{12} )^{156} - 1 }{\frac{0.0379}{12} }[/tex]
⇒21,200 = [tex]PMT\frac{(1 + 0.00315834 )^{156} - 1 }{0.00315834 }[/tex]
⇒21,200 = [tex]PMT\frac{(1.00315834 )^{156} - 1 }{0.00315834 }[/tex]
⇒21,200 = [tex]PMT\frac{1.635460826 - 1 }{0.00315834 }[/tex]
⇒21,200 = [tex]PMT\frac{0.635460826}{0.00315834 }[/tex]
⇒21,200 = PMT(201.2008924)
⇒PMT = [tex]\frac{21,200}{201.2008924}[/tex]
⇒PMT = 105.3673259 ≈ $105
∴ we get
They should deposit $105 every month so that they reach their goal.
