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
$2500 & 0.4 % & quarterly & 3 years
(i)
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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 3 years is $
Answer (2)
Calculate the quarterly interest rate: q u a r t er l y _ r a t e = 4 0.004 = 0.001 .
Calculate the number of compounding periods: n u m _ p er i o d s = 3 × 4 = 12 .
Apply the compound interest formula: F u t u re _ Va l u e = 2500 × ( 1 + 0.001 ) 12 ≈ 2530.17 .
The amount of money in the account after 3 years is 2530.17 .
Explanation
Understanding the Problem We are given a principal amount of $2500 deposited in a savings account with an annual interest rate of 0.4%, compounded quarterly for 3 years. We need to find the amount of money in the account after 3 years.
Calculating the Quarterly Interest Rate First, we need to find the quarterly interest rate. Since the annual interest rate is 0.4%, we divide this by 4 to get the quarterly interest rate: q u a r t er l y _ r a t e = 4 0.4% = 4 0.004 = 0.001
Calculating the Number of Compounding Periods Next, we need to find the number of compounding periods. Since the interest is compounded quarterly for 3 years, we multiply the number of years by 4 to get the number of compounding periods: n u m _ p er i o d s = 3 × 4 = 12
Applying the Compound Interest Formula Now, we can use the compound interest formula to calculate the future value of the investment: F u t u re _ Va l u e = P r in c i p a l × ( 1 + q u a r t er l y _ r a t e ) n u m _ p er i o d s Substituting the given values, we have: F u t u re _ Va l u e = 2500 × ( 1 + 0.001 ) 12 F u t u re _ Va l u e = 2500 × ( 1.001 ) 12 F u t u re _ Va l u e ≈ 2500 × 1.012067
Calculating the Future Value Calculating the future value: F u t u re _ Va l u e ≈ 2530.1675 Rounding to the nearest cent, we get: F u t u re _ Va l u e ≈ 2530.17
Final Answer Therefore, the amount of money in the account after 3 years is approximately $2530.17.
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 savings or investments will grow over time. It's also crucial for understanding loans, mortgages, and other financial products where interest is involved. Knowing how interest works can empower you to make informed decisions about your financial future.
After 3 years, the amount of money in the account will be approximately $2530.17, calculated using the compound interest formula with a $2500 principal, a 0.4% annual interest rate, and quarterly compounding. The quarterly interest rate is 0.001, and there are 12 compounding periods. Applying these values, we find the future value of the investment.
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