$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
[tex]\boxed{ \ A = P(1 + \frac{r}{n})^{nt} \ }[/tex]
- 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.
[tex]\boxed{ \ A = 3,050(1 + \frac{0.08}{4})^{(4)(25)} \ }[/tex]
[tex]\boxed{ \ A = 3,050(1.02)^{100} \ }[/tex]
[tex]\boxed{ \ A = 3,050 \times 7.244646 \ }[/tex]
[tex]\boxed{ \ A = 22,096.1703 \approx 22,096.17 \ }[/tex]
Thus the final amount that is put into a savings account for 25 years is $22,096.17
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