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

Anthony needs to invest $99.33.

Explanation:

The compound interest formula is given by:

`A(t) = P(1 + (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 + (r)/(n))^(nt)`

`130 = P(1 + (0.027)/(4))^(4*10)`

`P = (130)/((1 + (0.027)/(4))^(4*10))`

`P = 99.33`

Anthony needs to invest $99.33.