Question

Use the compound interest formula A(t)=P(1+ \frac{r}{n})^{nt}

Round to the hundredths place, if necessary. Do not include commas in your answers.



After a certain number of years, the value of an investment account is represented by the equation 10250(1+ \frac{0.04}{12})^{120} what is the value of the account? Answer

What was the initial deposit made to the account? Answer

How many years had the account been accumulating interest? Answer

Answer 1

To find the value of the investment account, we can use the compound interest formula:

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

Given information:

A(t) = 10250

P = Initial deposit

r = Interest rate per period = 0.04

n = Number of compounding periods per year = 12

t = Number of years = 120

1. Value of the account:

Plug in the given values into the compound interest formula:

10250 = P(1 + \frac{0.04}{12})^{120}

Calculate the right side of the equation:

(1 + \frac{0.04}{12})^{120} ≈ 1.601030112

10250 = P(1.601030112)

Divide both sides of the equation by (1.601030112) to solve for P:

P ≈ \frac{10250}{1.601030112}

The value of the account is approximately $6391.79.

2. Initial deposit:

The initial deposit made to the account is the value of P obtained in the previous step. Therefore, the initial deposit is approximately $6391.79.

3. Years the account has been accumulating interest:

The number of years the account has been accumulating interest is given as t = 120.

To summarize:

1. The value of the account is approximately $6391.79.

2. The initial deposit made to the account is approximately $6391.79.

3. The account has been accumulating interest for 120 years.

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