Liz and Bob just had a baby named Isabelle, and they

Ответ:

cahree

17.04.2021

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 = $PMT\frac{(1 + i)^{n} - 1 }{i}$

Here , we have

i = $\frac{\frac{3.79}{100} }{12} = \frac{{0.0379} }{12}$

n = 12×(18 - 5) = 156

Future value = 21,200.00

∴ we get

21,200.00 = $PMT\frac{(1 + \frac{0.0379}{12} )^{156} - 1 }{\frac{0.0379}{12} }$

⇒21,200 = $PMT\frac{(1 + 0.00315834 )^{156} - 1 }{0.00315834 }$

⇒21,200 = $PMT\frac{(1.00315834 )^{156} - 1 }{0.00315834 }$

⇒21,200 = $PMT\frac{1.635460826 - 1 }{0.00315834 }$

⇒21,200 = $PMT\frac{0.635460826}{0.00315834 }$

⇒21,200 = PMT(201.2008924)

⇒PMT = $\frac{21,200}{201.2008924}$

⇒PMT = 105.3673259 ≈ $105

∴ we get

They should deposit $105 every month so that they reach their goal.

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