Calculate the future value of the following:
o $5,000 compounded annually at 6% for 5 years
o $5,000 compounded semiannually at 6% for 5 years
o $5,000 compounded quarterly at 6% for 5 years
o $5,000 compounded annually at 6% for 6 years
• Answer the following: What conclusions can be drawn about the frequency of compounding interest? What conclusions can be drawn about the length of time an amount is compounding?
•
Please help, as I'm at a loss here.
Thanks for your help
The first answer is 5000*(1.06)^5
The second answer is 5000(1.03)^10
The third answer is 5000*(1.015)^20
The fourth answer is 5000*(1.06)^6
Do the numbers and draw your own conclusions.
$5,000 compounded semiannually at 6% for 5 years
Compute the amount that a $15,000 investment today would accumulate at 9% (compound interest) by the en of 6 years.
To calculate the future value of an amount compounded at a given interest rate for a certain number of years, you can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (the initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
Let's calculate the future value for each given scenario:
1. $5,000 compounded annually at 6% for 5 years:
Using the formula, we have:
A = 5,000(1 + 0.06/1)^(1*5) = $6,644.74
2. $5,000 compounded semiannually at 6% for 5 years:
Using the formula, we have:
A = 5,000(1 + 0.06/2)^(2*5) = $6,678.66
3. $5,000 compounded quarterly at 6% for 5 years:
Using the formula, we have:
A = 5,000(1 + 0.06/4)^(4*5) = $6,692.85
4. $5,000 compounded annually at 6% for 6 years:
Using the formula, we have:
A = 5,000(1 + 0.06/1)^(1*6) = $6,822.72
Conclusion about the frequency of compounding interest:
As the frequency of compounding increases (from annually to semiannually to quarterly in the given scenarios), the future value of the investment increases. This means that more frequent compounding leads to higher overall returns.
Conclusion about the length of time an amount is compounding:
As the length of time an amount is compounding increases (from 5 years to 6 years in the given scenarios), the future value of the investment also increases. This demonstrates that more time allows for greater growth and accumulation of interest on the investment.
In summary, more frequent compounding and longer periods of time both contribute to higher future values in compound interest calculations.