Question

Suppose that a family wants to start a college fund for their child. if they can get a rate of 5.5% , compounded monthly, and want the fund to have a value of $35,450 after 20 years, how much should they deposit monthly? assume an ordinary annuity and round to the nearest cent. a. $81.38 b. $80.01 c. $11,829.97 d. $11,776.00 please select the best answer from the choices provided a b c d

Answer 1

Explanation:

We know that,

`➟\sf \: fv \: of \: annuity \: = p( \frac{(1 + r) {}^(n) - 1}{r} )`

where,

FV of annuity = $35,450

P = monthly payment,

r = rate of interest = 5.5% annually =
`(5.5)/(12)%`

n = number period = 20 years = 240 months

Putting all the values,

`\sf35450 = p( \frac{(1 + (0.055)/(12) ) {}^(240) - 1}{ (0.055)/(12) } )`

`\sf \: p = \frac{35450}{( \frac{(1 + (0.055)/(12) ) {}^(240) - 1}{ (0.055)/(12) } )}`

`\sf \: p \: = \: \$81.36`

Therefore, they should deposit $81.38 monthly.