Question

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. How much should they deposit every month so that they reach their goal

Answer 1

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

Step-by-step 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((1 + i)^(n) - 1 )/(i)`

Here , we have

i =
`((3.79)/(100) )/(12) = \frac{{0.0379} }{12}`

n = 12×(18 - 5) = 156

Future value = 21,200.00

∴ we get

21,200.00 =
`PMT((1 + (0.0379)/(12) )^(156) - 1 )/((0.0379)/(12) )`

⇒21,200 =
`PMT((1 + 0.00315834 )^(156) - 1 )/(0.00315834 )`

⇒21,200 =
`PMT((1.00315834 )^(156) - 1 )/(0.00315834 )`

⇒21,200 =
`PMT(1.635460826 - 1 )/(0.00315834 )`

⇒21,200 =
`PMT(0.635460826)/(0.00315834 )`

⇒21,200 = PMT(201.2008924)

⇒PMT =
`(21,200)/(201.2008924)`

⇒PMT = 105.3673259 ≈ $105

∴ we get

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