The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b).
| Principal | Rate | Compounded | Time |
| --------- | ------ | ---------- | ------- |
| $7000 | 0.6% | quarterly | 5 years |
(i) Click the icon to view some finance formulas.
a. Find how much money there will be in the account after the given number of years.
The amount of money in the account after 5 years is $ [ ] (Round to the nearest cent as needed.)
Answer (2)
Calculate the quarterly interest rate: r = 4 0.6% = 0.0015 .
Calculate the number of compounding periods: n = 5 × 4 = 20 .
Apply the compound interest formula: A = 7000 ( 1 + 0.0015 ) 20 .
The amount of money in the account after 5 years is approximately 7213.02 .
Explanation
Understanding the Problem We are given a principal amount of $7000 deposited in a savings account with an annual interest rate of 0.6% compounded quarterly for 5 years. We need to find the amount of money in the account after 5 years.
Calculating the Quarterly Interest Rate First, we need to determine the quarterly interest rate. Since the annual interest rate is 0.6%, the quarterly interest rate is calculated by dividing the annual rate by 4: r = 4 0.6% = 0.15% = 0.0015
Calculating the Number of Compounding Periods Next, we need to find the number of compounding periods. Since the interest is compounded quarterly for 5 years, the total number of compounding periods is: n = 5 years × 4 quarters/year = 20 quarters
Applying the Compound Interest Formula Now, we can use the compound interest formula to calculate the amount of money in the account after 5 years: A = P ( 1 + r ) n where:
A is the amount of money after n years
P is the principal amount ($7000)
r is the quarterly interest rate (0.0015)
n is the number of compounding periods (20)
Calculating the Final Amount Substituting the values into the formula, we get: A = 7000 ( 1 + 0.0015 ) 20 A = 7000 ( 1.0015 ) 20 A ≈ 7000 × 1.03040655 A ≈ 7212.84585 Rounding to the nearest cent, we get $7212.85.
Final Answer Therefore, the amount of money in the account after 5 years is approximately $7212.85.
Examples
Compound interest is a powerful concept used in many real-life financial situations. For example, when you deposit money into a savings account, the bank pays you interest, which is often compounded. Understanding compound interest helps you estimate how much your investments will grow over time. It's also crucial for understanding loans, mortgages, and other financial products where interest is charged on the principal and accumulated interest.
After calculating the compound interest for an initial deposit of $7000 at a rate of 0.6% compounded quarterly over 5 years, the amount in the account is approximately $7212.85. This includes determining the quarterly interest rate and the total number of compounding periods. By applying the compound interest formula, we find the total accumulated amount after the specified period.
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