Question

Omar wants to open an account for his grandchildren that he hopes will have
$80,000 in it after 20 years. How much must he deposit now into an account
that yields 1.75% interest, compounded monthly, so he can be assured of
reaching his goal?

Answer 1

Using compound interest, it is found that he must deposit $56,389.

Compound interest:

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

• A(t) is the amount of money after t years.  
• 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.  
• t is the time in years for which the money is invested or borrowed.

In this problem:

• Hopes to have $80,000 in 20 years, thus $t = 20, A(t) = 80000$.
• Interest rate of 1.75%, thus $r = 0.0175$.
• Compounding monthly, thus $n = 12$
• The investment is of P, for which we have to solve.

Then:

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

$80000 = P(1 + \frac{0.0175}{12})^{12(20)}$

$P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}$

$P = 56389$

He must deposit $56,389.

A similar problem is given at https://brainly.com/question/25263233