Question

1. The parents of a 5-year old child wish to have $250,000 when the child starts
college at the age of 18. How much should they deposit monthly in an account
that pays 4.5% compounded monthly to achieve their goal?

2.
A 25-year old saves for retirement by making monthly deposits of $1000 in an
account that pays 4.9% compounded monthly. How much would be in the account
at retirement age of 65?

please solve asap

i will appreciate your help and will give thumbs up

Answer 1

1.

Given,

Future value = $250000

Interest rate = 4.5% or 0.045

No. of years = 13 years (from age 5 to age 18)

Solution :-

Monthly interest rate (r) = 0.045/12 = 0.00375

No. of months (n) = 13 years x 12 months = 156 months

Now,

Monthly deposit = (Future value x r) [(1 + r)ⁿ - 1]

= ($250000 x 0.00375) [(1 + 0.00375)¹⁵⁶ - 1]

= $937.50 [(1.00375)¹⁵⁶ - 1]

= $937.50 [1.793028087 - 1]

= $937.50 0.793028087 = $1182.18

So, they should deposit $1182.18 monthly to achieve their goal.