Question

Jake's parents want to save for his college tuition and will make equal payments over the next ten years. they have estimated that they will need $75,000 by the time jake starts college and can earn five percent. how much money will jake's parents need to deposit each year to have this amount by the time jake graduates from high school?

Answer 1

$5962.85
The formula for value of an investment with periodic deposits is:
A = M((1 + i/q)^(nq) - 1)(q/i)
where
A = value
M = amount of deposit per period
i = interest rate
q = number of periods per year
n = number of years

Let's assume one period per year to simplify, giving
A = M((1 + i)^(n) - 1)(1/i)
A = M((1 + i)^(n) - 1)/i

Now solve for M, then substitute the known values and calculate:
A = M((1 + i)^(n) - 1)/i
Ai = M((1 + i)^(n) - 1)
Ai/((1 + i)^(n) - 1) = M

75000 * 0.05/ ((1 + 0.05)^(10) - 1) = M
3750/ (1.05^10 - 1) = M
3750/ (1.628894627 - 1) = M
3750/ 0.628894627 = M
5962.843122 = M

So the amount Jake's parents need to deposit each year is $5962.85