Question

Porsha calculates the amount of money she will have at the end of 6 years on a $5,000 investment earning 3.75% interest compounded quarterly. She writes the following expression: Which of the following statements about Porsha's expression is true? a. Porsha's expression is correct. b. Porsha's expression should have 1 + 0.009375 in the parentheses. c. Porsha's expression should have an exponent of 6, not 24. d. Porsha's expression should have both 1 + 0.009375 in the parentheses and an exponent of 6.

Answer 1

It is B. Porsha's expression should have 1 + 0.009375 in the parentheses.

Explanation:

I got it in the test

Answer 2

Invested amount = $5,000.

Interest rate = 3.75% per year compounded quarterly, that is 4 times in a year.

First we would convert percentage into decimals 3.75%=3.75/100 = 0.0375.

Because interest is compounded quarterly, we need to divide 0.0375 by 4, we get 0.009375.

Number of years = 6 years.

n=4 (number of quarters in a year)

We can apply Compound interest formula.

`A=P(1+r/n)^(n*t)`, Where P is invested amount, r is the rate of interest, it is the time in number of years and n is the number of installments.

Plugging values of P, r, t and n in above formula, we get

A = 5,000 ( 1+
`( 0.0375)/(4)`)
`^(6*4)`

0.0375 divided by 4 gives 0.009375 and 6*4 = 24.

So, we could rewrite expression as,

`A=5000(1+0.009375)^(24).`

We can add 1+0.009375, we get 1.009375.

`A=5000(1.009375)^(24).`

Expression could be written in any form

`A=5,000(1+(0.0375)/(4))^(6*4)` or

`A=5000(1+0.009375)^(24)` or

`A=5000(1.009375)^(24)`.