Final answer:
To find the value of the investment at the end of years, we can use the formula for compound interest. For daily compounding, the value is approximately $28,964.59 and for monthly compounding, the value is approximately $28,987.27.
Step-by-step explanation:
To find the value of the investment at the end of a given number of years with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
For daily compounding, n = 365, and for monthly compounding, n = 12.
Let's calculate the value of the investment for each compounding method.
For daily compounding:
A = $27,100(1 + 0.07/365)^(365*years)
Substituting years = 1 into the formula:
A = $27,100(1 + 0.07/365)^(365)
Calculating the value of the investment using a calculator or spreadsheet, the answer is approximately $28,964.59.
For monthly compounding:
A = $27,100(1 + 0.07/12)^(12*years)
Substituting years = 1 into the formula:
A = $27,100(1 + 0.07/12)^(12)
Calculating the value of the investment using a calculator or spreadsheet, the answer is approximately $28,987.27.