Final answer:
The future value of $200 deposited at a semi-annual interest rate of 8% for three years can be calculated using the compound interest formula A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
Step-by-step explanation:
The future value of $200 received today and deposited for three years in an account which pays semi-annual interest of 8% can be calculated using the compound interest formula: A = P(1 + r/n)nt, where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case:
- P = $200
- r = 0.08 (8% expressed as a decimal)
- n = 2 (since the interest is compounded semi-annually)
- t = 3 years
Therefore, the future value A is calculated as follows:
A = 200(1 + 0.08/2)2*3
Use a calculator to find the value of A, which will be the total amount of money you will have after 3 years, including the compounded interest.