Question

Amelia is going to invest in an account paying an interest rate of 2.3% compounded quarterly. How much would Amelia need to invest, to the nearest hundred dollars, for the value of the account to reach $1,530 in 19 years?

Answer 1

Answer:

Amelia needs to invest $989.57.

Step-by-step explanation:

The compound interest formula is given by:

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

Where 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 and t is the time in years for which the money is invested or borrowed.

Amelia is going to invest in an account paying an interest rate of 2.3% compounded quarterly.

This means that $r = 0.023, n = 4$.

How much would Amelia need to invest, to the nearest hundred dollars, for the value of the account to reach $1,530 in 19 years?

We have to find P for which $A(t) = 1530$ when $t = 19$. So

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

$1530 = P(1 + \frac{0.023}{4})^{4*19}$

$P = \frac{1530}{(1 + \frac{0.023}{4})^{4*19}}$

$P = 989.57$

Amelia needs to invest $989.57.