Kendra signed a contract to play professional soccer. She got a $100,000 signing bonus, and she decided to invest the bonus in a money market account that pays 15% interest compounded yearly. She plans to use the signing bonus when she retires in 20 years. How much will her investment be worth in 20 years? Round the answer to two decimal places.(1 point)
To find out how much Kendra's investment will be worth in 20 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (or the future value of the investment)
P = the principal amount (or 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, the principal amount is $100,000, the annual interest rate is 15% (or 0.15 as a decimal), the interest is compounded yearly (so n = 1), and the number of years we're interested in is 20.
Plugging in these values into the formula, we get:
A = 100,000(1 + 0.15/1)^(1*20)
A = 100,000(1.15)^20
Calculating this expression, we find that A is approximately $3,172,840.65.
Therefore, Kendra's investment will be worth approximately $3,172,840.65 in 20 years.
this is wrong
Apologies for the mistake. Let's recheck the calculation.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (or future value of the investment)
P = the principal amount (or 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, the principal amount is $100,000, the annual interest rate is 15% (or 0.15 as a decimal), the interest is compounded yearly (so n = 1), and the number of years is 20.
Plugging in these values into the formula:
A = 100,000(1 + 0.15/1)^(1*20)
A = 100,000(1.15)^20
Calculating this expression, we find that A is approximately $1,596,848.08.
Therefore, Kendra's investment will be worth approximately $1,596,848.08 in 20 years.
still wrong
Apologies for the repeated mistakes. Let's recheck the calculation.
Using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (or future value of the investment)
P = the principal amount (or 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, the principal amount is $100,000, the annual interest rate is 15% (or 0.15 as a decimal), the interest is compounded yearly (so n = 1), and the number of years is 20.
Plugging in these values into the formula:
A = 100,000(1 + 0.15/1)^(1*20)
A = 100,000(1.15)^20
Calculating the expression, we find that A is approximately $1,828,783.65.
Therefore, Kendra's investment will be worth approximately $1,828,783.65 in 20 years.
To calculate the future value of Kendra's investment after 20 years, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Kendra's principal amount (P) is $100,000, the interest rate (r) is 15% (or 0.15 in decimal form), the number of times interest is compounded per year (n) is once (since it is compounded yearly), and the number of years (t) is 20.
Substituting the values into the formula, we get:
A = 100,000(1 + 0.15/1)^(1*20)
Simplifying further:
A = 100,000(1 + 0.15)^20
Calculating the expression within the parentheses first:
A = 100,000(1.15)^20
Using a calculator or a spreadsheet, raise 1.15 to the power of 20 and multiply the result by 100,000:
A ≈ 1.1725979 * 100,000
A ≈ 117,259.79
Therefore, her investment will be worth approximately $117,259.79 after 20 years.
(Note: Since the question asks to round the answer to two decimal places, the final answer would be $117,259.79)