Pls Help. Not too sure how to do this question.
Someone wants to set aside money for their newborn daughters college funds. He estimates she would need 25,000 on her 17, 18, 19 and 20, birthdays. If he plans to make uniform deposits starting 3 years from now and through her 16 birthday, what should the size of the deposit be if it acumulates interest at a rate of 10% per year?
i have a chart which will give me P/A or F/A etc. just don't know the steps. pls help thanks!
To answer this question, we will use the "Uniform Series Compound Amount" formula, also known as the future value of an ordinary annuity. This formula allows us to calculate the accumulated value of a uniform series of deposits over a certain period of time with compound interest.
The formula for the future value of an ordinary annuity is:
F = P((1 + r)^n - 1) / r
Where:
F = Future value (the accumulated amount)
P = Uniform deposit (the size of the deposit)
r = Interest rate per period (in this case, 10% per year or 0.10)
n = Number of periods (in this case, 16 years)
In this problem, the uniform deposits start 3 years from now and continue until the daughter's 16th birthday, which gives us a total of 16 years of deposits.
We know that the desired amount on each birthday is $25,000, and there are four birthdays in total, so the total desired amount is 4 * $25,000 = $100,000.
Let's plug in the values into the formula and solve for P:
$100,000 = P((1 + 0.10)^16 - 1) / 0.10
First, let's simplify the equation inside the parentheses:
1.10^16 - 1
Using a calculator, we find that 1.10^16 is approximately 4.177
Now we can rewrite the equation:
$100,000 = P(4.177 - 1) / 0.10
$100,000 = P(3.177) / 0.10
Next, isolate P:
$100,000 * 0.10 = P * 3.177
$10,000 = P * 3.177
Now, solve for P by dividing both sides by 3.177:
P = $10,000 / 3.177
Using a calculator, we find that P ≈ $3,145.25
Therefore, the size of the deposit should be approximately $3,145.25 if it accumulates interest at a rate of 10% per year.
Remember, this answer assumes that the interest is compounded annually and is not affected by any external factors.