Final answer:
The total amount of a $2700 investment compounded annually at 12% for 1 year is found using the compound interest formula for different conditions. Substitutions into the formula yield the future values of $3024, $3386.88, $3042.36, and $3421.03 for scenarios a), b), c), and d) respectively.
Step-by-step explanation:
The compound interest formula A=P(1+r/n)^(nt) is used to calculate the future value of an investment. The variables in the formula represent the following: P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years the money is invested. To find the total amount when $2700 is compounded annually at 12% for various periods and compounding frequencies, we'll substitute the given values into the formula and solve.
- For part a), the total amount for P = $2700, r = 0.12, n = 1, and t = 1 is calculated as A = 2700(1+0.12/1)^(1*1) = 2700(1.12)^1 = $3024.
- For part b), with the same principal, rate, and compounding frequency but over 2 years (t = 2), the total amount is A = 2700(1.12)^2 = $3386.88.
- For part c), with biannual compounding (n = 2) over 1 year, the total amount is A = 2700(1+0.12/2)^(2*1) = 2700(1.06)^2 = $3042.36.
- For part d), with biannual compounding over 2 years, the total amount is A = 2700(1+0.12/2)^(2*2) = 2700(1.06)^4 = $3421.03.