Question

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Anthony is going to invest in an account paying an interest rate of 2.7% compounded
quarterly. How much would Anthony need to invest, to the nearest hundred dollars,
for the value of the account to reach $130 in 10 years?
Answer:
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Answer 1

Answer:

Anthony needs to invest $99.33.

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.

Interest rate of 2.7% compounded quarterly.

This means that $r = 0.027, n = 4$.

How much would Anthony need to invest, to the nearest hundred dollars, for the value of the account to reach $130 in 10 years?

We have to find P for which: $A = 130, t = 10$. So

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

$130 = P(1 + \frac{0.027}{4})^{4*10}$

$P = \frac{130}{(1 + \frac{0.027}{4})^{4*10}}$

$P = 99.33$

Anthony needs to invest $99.33.