Compound interest word problem.
Suppose JJ has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does JJ have at the end of 5 years?
Formula:
A= The amount of money earned after a certain length of time.
P= The amount of money you start with, the principal.
r= The interest rate, in decimal.
t= The amount of time over which the interest is compounded.
n= The number of times the interest in compounded in one year.
A=P(1+r/n)^nt
How do I answer and show work with question, using the formula?
Everything you need for the formula is given.
A = 1000
r = .035
t = 5
n = 4
A=P(1+r/n)^nt
= 1000(1 + .035/4)^20
= ....
you do the button-pushing
To answer the question and show the work using the given formula, follow these steps:
Step 1: Identify the given values:
- Principal amount (P): $1000
- Interest rate (r): 3.5% (convert to decimal by dividing by 100, giving 0.035)
- Time (t): 5 years
- Compounding frequency (n): quarterly (4 times per year)
Step 2: Plug in the values into the formula:
A = P(1 + r/n)^(nt)
A = $1000(1 + 0.035/4)^(4*5)
Step 3: Simplify and calculate:
Since the interest is compounded quarterly (n = 4), we first need to divide the annual interest rate (0.035) by 4.
A = $1000(1 + 0.00875)^(20)
A = $1000(1.00875)^(20)
Now, calculate the value inside the parentheses (1.00875 raised to the power of 20) using either a calculator, spreadsheet software, or by multiplying the number repeatedly:
A ≈ $1000(1.19318)
A ≈ $1,193.18
Therefore, at the end of 5 years, JJ would have approximately $1,193.18 in the account.