Question

You want to provide spending money for your 4 year old during their college years. You can afford to deposit $600/year for the next 4 years (starting this year). You would like to give your child $4,000 per year for in their 18th, 19th, 20th, and 21st birthdays for a total of $16,000. Assuming 5% interest, what uniform annual investment will you have to make on the child's 8th through 17th birthdays to meet this goal

Answer 1

Answer:

The Annual investment that you will to make will be $1,069.01

Explanation:

In order to calculate the uniform annual investment that will you have to make on the child's 8th through 17th birthdays to meet this goal, we have to make the following calculations:

First we need to calculate the Amount you have at the end of child's 8th year = 600*(1+0.05)^4 + 600*(1+0.05)^3 + 600*(1+0.05)^2 + 600*(1+0.05)^1 = $2,715.38

Therefore, Value of this amount at the end of 17th year = $2715.38 * (1+0.05)^9 = $4,212.45

So, Amount required to be saved = $16,000 - $4,212.45 = $11,787.55

Therefore, to calculate the annual investment we would have to use the following formula:

FV of annuity = P*[((1+r)^n - 1)/r]

P - Periodic payment =?

r - rate per period = 0.05

n - number of periods = 17-8 = 9

$11787.55 = P*(((1+0.05)^9 - 1)/0.05)

P = $11,787.55/11.03 = $1,069.01

The Annual investment that you will to make will be $1,069.01