Question

K

The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total
amount due at time t.
P = $9000, r = 5.5%, t = 8 months
The future value is $
(Simplify your answer. Type an integer or a decimal.)
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Answer 1

we know that a year has 12 months, so 8 months is really 8/12 of a year.

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9000\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ t=years\to (8)/(12)\dotfill &(2)/(3) \end{cases} \\\\\\ A = 9000[1+(0.055)((2)/(3))] \implies A = 9330`

Answer 2

the future value or total amount due at the end of 8 months is $9,330.00

Explanation:

To find the future value of a loan that is borrowed at a simple interest rate, we use the formula:

A = P(1 + rt)

where A is the future value or total amount due, P is the principal or initial amount borrowed, r is the simple interest rate as a decimal, and t is the time period in years.

In this case, the principal is $9000, the simple interest rate is 5.5% or 0.055 as a decimal, and the time period is 8 months or 8/12 = 2/3 years.

Substituting these values into the formula, we get:

A = 9000(1 + 0.055 × 2/3)

= 9000(1.0375)

= $9,330.00

Therefore, the future value or total amount due at the end of 8 months is $9,330.00