Marcus invests $8,000, at 8% interest, compounded annually for 15 years. Calculate the compound interest for his investment.
Just add 8% every year.
just as a hint, adding 8% every year means multiplying by 1.08 for each year, not adding 8% of the original 8000.
To calculate the compound interest for Marcus' investment, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Marcus invests $8,000 at an 8% interest rate, compounded annually for 15 years.
P = $8,000
r = 8% = 0.08
n = 1 (compounded annually)
t = 15
Substituting the values into the formula:
A = 8000(1 + 0.08/1)^(1*15)
A = 8000(1 + 0.08)^15
A = 8000(1.08)^15
Using a calculator, we can find:
A ≈ $21,589.84
To calculate the compound interest, we subtract the principal amount from the final amount:
Compound Interest = A - P
Compound Interest = $21,589.84 - $8,000
Compound Interest ≈ $13,589.84
Therefore, the compound interest for Marcus' investment is approximately $13,589.84.
To calculate the compound interest for Marcus' investment, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, Marcus invested $8,000 at an annual interest rate of 8% for 15 years, compounded annually. So we have:
P = $8,000
r = 8% = 0.08 (as a decimal)
n = 1 (compounded annually)
t = 15 years
Plugging the values into the formula:
A = 8000(1 + 0.08/1)^(1*15)
Calculating inside the parentheses first:
1 + 0.08/1 = 1.08
Now, we raise this value to the power of 15:
1.08^15 ≈ 2.9796
Finally, multiply this result by the principal amount:
A ≈ 8000 * 2.9796 ≈ $23,837.60
The future value of Marcus' investment after 15 years is approximately $23,837.60.
To find the compound interest, we subtract the initial investment from the future value:
Compound Interest = Future Value - Principal Amount
Compound Interest = $23,837.60 - $8,000
Compound Interest ≈ $15,837.60
Therefore, the compound interest for Marcus' investment is approximately $15,837.60.