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.

Answer 1

Answer:

They should deposit $81.38 monthly.

Step-by-step explanation:

We know that,

$\text{FV of annuity}=P\left(\dfrac{(1+r)^n-1}{r}\right )$

where,

FV of annuity = $35,450

P = monthly payment,

r = rate of interest = 5.5% annually = $\dfrac{5.5}{12}\%$

n = number period = 20 years = 240 months

Putting all the values,

$\Rightarrow 35450=P\left(\dfrac{(1+\frac{0.055}{12})^{240}-1}{\frac{0.055}{12}}\right )$

$\Rightarrow P\dfrac{35450}{\left(\dfrac{(1+\frac{0.055}{12})^{240}-1}{\frac{0.055}{12}}\right )}$

$\Rightarrow P=\ 81.38$

Therefore, they should deposit $81.38 monthly.

Answer 2

In 20 years a family will be able to earn 35 450 dollars. The interest that they earned is 5.5% compounded monthly. Now, let's find out how much will they need to save monthly to get this amount in 20 year:
=> 12 * 20 = 240 months
=> 35 450 / 240 months = 147.7 dollars per month is the money with interest
Let's subtract the interest
=> 147.7 * 0.055 = 8.1 dollars.
=> 147.7 - 8.1 = 139.6 dollars per month.