What would be the value of a savings account started with [tex]$2,700, earning 5 percent (compounded annually) after 8 years?

Note: Use appropriate factor(s) from the tables provided. Round the time value factor to 3 decimal places and the final answer to 2 decimal places.

Value of savings account:

[tex] \text{Value of savings account} = \$[/tex] \_\_\_\_\_\_ \]



Answer :

To find the value of a savings account started with [tex]$2,700, earning 5 percent interest compounded annually after 8 years, we can make use of the compound interest formula. The compound interest formula is given by: \[ A = P \left(1 + \frac{r}{n}\right)^{n \cdot t} \] where: - \( A \) is the amount in the savings account after the specified time. - \( P \) is the principal amount (initial deposit), which is $[/tex]2,700.
- [tex]\( r \)[/tex] is the annual interest rate (decimal form), which is 0.05 for 5%.
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year. Since the interest is compounded annually, [tex]\( n = 1 \)[/tex].
- [tex]\( t \)[/tex] is the number of years the money is invested, which is 8 years in this case.

Applying these values to the formula:

[tex]\[ A = 2700 \left(1 + \frac{0.05}{1}\right)^{1 \times 8} \][/tex]

Simplify the expression inside the parentheses:

[tex]\[ A = 2700 \left(1 + 0.05\right)^8 \][/tex]

[tex]\[ A = 2700 \left(1.05\right)^8 \][/tex]

Now, compute [tex]\( (1.05)^8 \)[/tex]. From the training and given the result, we know:

[tex]\( (1.05)^8 \approx 1.477 \)[/tex]

So the equation becomes:

[tex]\[ A = 2700 \times 1.477 \][/tex]

Finally, perform the multiplication:

[tex]\[ A = 3989.13 \][/tex]

Thus, the value of the savings account after 8 years is $3,989.13.