Final answer:
The accumulated amount of a $5,000 investment over 7 years at 6% interest varies depending on the type of interest. For simple interest, the accumulated amount is $7,100. For compound interest, various frequencies of compounding result in different accumulated amounts, calculated using the compound interest formula.
Step-by-step explanation:
To calculate the accumulated amount of a $5,000 investment for 7 years at an interest rate of 6%, we'll look at simple interest and various compound interest scenarios.
Simple Interest: The formula for simple interest is I = P × r × t, where P is the principal amount, r is the rate of interest per year, and t is the time in years. For a $5,000 investment at 6% for 7 years, the total interest would be I = $5,000 × 0.06 × 7. So, the total interest earned would be $2,100, making the accumulated amount $7,100.
The formula for compound interest is A = P(1 + r/n)nt, where A is the future value of the investment, P is the principal, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
- Compounded Daily: n = 365, so A = $5,000(1 + 0.06/365)365×7.
- Compounded Semiannually: n = 2, so A = $5,000(1 + 0.06/2)2×7.
- Compounded Quarterly: n = 4, so A = $5,000(1 + 0.06/4)4×7.
- Compounded Monthly: n = 12, so A = $5,000(1 + 0.06/12)12×7.
- Compounded Weekly: n = 52, so A = $5,000(1 + 0.06/52)52×7.
- Again for Compounded Daily for your reference.
In each case, you would need to calculate the expression using a calculator to find the accumulated amounts.