Question

What lump sum do parents need to deposit in an account earning 9%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 13 years? (Round your answer to the nearest cent.)

Answer 1

Answer:

They need to deposit $31,172.49

Step-by-step explanation:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time the money is invested or borrowed for, in years.

In this problem

We want to find P for which $A = 100000$ when $r = 0.09, n = 12, t = 13$

So

$A = P(1 + \frac{r}{n})^{nt}$

$100000 = P(1 + \frac{0.09}{12})^{12*13}$

$3.208P = 100000$

$P = \frac{100000}{3.208}$

$P = 31172.49$

They need to deposit $31,172.49