1. Find the compound amount and the interest earned for the following: Amount: $980 Rate: 8%, compounded quarterly Time: 5 years
2. Find the interest earned if $2750 is deposited on June 12 and withdrawn on August 30. Assume 3.5% interest compounded daily.
3. Find the present value for the following: Amount needed: $20,000 Time: 10 years Rate: 5%, compounded semiannually
4. What is the effect of inflation on spendable income?
s. Application Problem: Describe a practical example where you do, or could, use the concepts of compound interest found in this chapter in your life.



Sample Answer

Sample Answer


Title: Unraveling the World of Compound Interest: Calculations and Real-Life Applications

Compound Amount and Interest Earned:Amount: $980
Rate: 8%
Compounded Quarterly
Time: 5 years

To calculate the compound amount and interest earned, we can use the formula for compound interest:
[ A = P(1 + \frac{r}{n})^{nt} ]


A = Amount after t years
P = Principal amount ($980)
r = Annual interest rate (8% or 0.08)
n = Number of times interest is compounded per year (quarterly, so 4)
t = Time in years (5)

Plugging in the values:
[ A = 980(1 + \frac{0.08}{4})^{4*5} ]
[ A = 980(1 + 0.02)^{20} ]
[ A ≈ 980(1.02)^{20} ]
[ A ≈ 980 * 1.48594673 ]
[ A ≈ $1,456.03 ]

To find the interest earned:
Interest = Compound Amount – Principal
Interest = $1,456.03 – $980
Interest ≈ $476.03

Interest Earned on Deposit and Withdrawal:Deposit Amount: $2750
Interest Rate: 3.5%
Compounded Daily
Time: June 12 to August 30

To calculate the interest earned, we can use the formula for compound interest with the given dates in mind.

Present Value Calculation:Amount Needed: $20,000
Rate: 5%
Compounded Semiannually
Time: 10 years

To find the present value, we need to determine how much money needs to be invested now to reach $20,000 in 10 years with a semiannual compounding interest rate of 5%.

Effect of Inflation on Spendable Income:
Inflation erodes the purchasing power of money over time, meaning that the same amount of money will buy fewer goods and services as time goes on. This decrease in purchasing power reduces the spendable income of individuals, as they need more money to maintain the same standard of living.

Real-Life Application of Compound Interest:
One practical example where compound interest concepts come into play is in long-term savings or investments, such as retirement funds or college savings plans. By understanding how compound interest works, individuals can make informed decisions about where to invest their money to maximize growth over time. For instance, contributing regularly to a retirement account and taking advantage of compounding can help build a substantial nest egg for the future.

In conclusion, compound interest calculations are not only essential for financial planning and decision-making but also have real-world applications that can significantly impact individuals’ financial well-being in the long run. Understanding these concepts empowers individuals to make informed choices about saving, investing, and managing their money effectively.

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