Question

what is the final amount of $3050.00 that is put into a savings account with 8% interest rate for 25 years, if the interest is compounded 4 times per year?

Answer 1

The formula required is:
$A=P(1+\frac{r}{n})^{nt}$
where A is the amount after t years of the principal P invested at an annual interest rate r (expressed as a decimal fraction) compounded n times per year.
Plugging in the given values, we get:
$A=3050(1+\frac{0.08}{4})^{(4\times25)}=22,096.17$
The final amount is $22,096.17

Answer 2

$22,096.17

Further explanation

Given:

• The initial amount = $3,050.00
• Time = 25 years
• Interest rate = 8%, therefore 8% equal to 0.08
• Compounded n = 4 times per year

Question:

What is the final amount?

The Process:

Compound interest is the interest earned from the initial amount and the interest earned previously. The formula for the balance A of the savings with compound interest is

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

• P = principal (initial amount)
• r = annual interest rate (in decimal form)
• t = time (in years)
• n = the number of periods of interest is compounded per year

Let us calculate the final amount.

$\boxed{ \ A = 3,050(1 + \frac{0.08}{4})^{(4)(25)} \ }$

$\boxed{ \ A = 3,050(1.02)^{100} \ }$

$\boxed{ \ A = 3,050 \times 7.244646 \ }$

$\boxed{ \ A = 22,096.1703 \approx 22,096.17 \ }$

Thus the final amount that is put into a savings account for 25 years is $22,096.17

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