Create a compound interest word problem. Be sure to include the following, leaving one of the variables unknown:
The amount of money earned after a certain length of time, A.
The amount of money you start with, the principal, P.
The interest rate, r.
The amount of time over which the interest is compounded, t.
The number of times the interest in compounded in one year, n.
A = P((1+r/n)^(nt)-1)
pick the one you want to leave unknown. See related questions for ideas on questions.
Sure! Here's a compound interest word problem:
Jenny decides to invest some money in a bank account that earns compound interest. She initially invests $5,000 in the account. The interest rate is 8% and it is compounded quarterly (four times per year). Jenny leaves the money in the account for 3 years.
To find out the amount of money earned after 3 years (A), we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
where:
- A is the amount of money earned after a certain length of time,
- P is the principal amount (the amount of money you start with),
- r is the interest rate,
- t is the time over which the interest is compounded, and
- n is the number of times the interest is compounded in one year.
Let's plug in the known values into the formula:
P = $5,000 (principal)
r = 8% (interest rate)
t = 3 years (time)
n = 4 (compounded quarterly)
Substituting these values into the formula:
A = $5,000 * (1 + 0.08/4)^(4*3)
Now, we can simplify the expression inside the parentheses:
1 + 0.08/4 = 1.02.
A = $5,000 * (1.02)^(12)
Now, let's calculate the final amount by raising (1.02) to the power of 12:
A = $5,000 * (1.02)^12
Using a calculator, we find that (1.02)^12 is approximately 1.268.
A ≈ $5,000 * 1.268
A ≈ $6,340.43
Therefore, after 3 years, Jenny will have approximately $6,340.43 in her bank account.