Question

You have decided to invest $761 into a savings account which pays an annual interest rate of 12%. What is the value of the 5 avings account in 5 years?

Answer 1

The value of the savings account in 5 years, with an annual interest rate of 12% on an initial investment of $761, can be calculated using the compound interest formula. The final amount, A, is given by:

`\[ A = P * (1 + r)^t \]`

where P is the principal amount, r is the interest rate per period, and t is the number of periods.

Step-by-step explanation:

In this scenario, P = $761, r = 0.12 (12% as a decimal), and t = 5 years. Substituting these values into the compound interest formula:

`\[ A = $761 * (1 + 0.12)^5 \]`

Now, calculate the value of
`\( (1 + 0.12)^5 \)` and then multiply it by $761 to find the final amount. This accounts for the compounding effect over the 5 years.

`\[ (1 + 0.12)^5 \approx 1.76234 \]`

`\[ A \approx $761 * 1.76234 \approx $1,342.81 \]`

Therefore, the value of the savings account in 5 years is approximately $1,342.81. This result reflects the compound growth of the initial investment over the specified time, taking into account the annual interest rate.