Question

  Sarah Wiggum would like to make a single investment and have ​$1.7 million at the time of her retirement in 34 years. She has found a mutual fund that will earn 7 percent annually. How much will Sarah have to invest​ today

Answer 1

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$

In this question:

$t = 35, I = 0.07, T = 1700000$

She has to invest P today.

$T = E + P$

$1700000 = E + P$

$E = 1700000 - P$

So

$E = P*I*t$

$1700000 - P = P*0.07*34$

$3.38P = 1700000$

$P = \frac{1700000}{3.38}$

$P = 502958.58$

Sarah has to invest $502,958.58 today.