Final answer:
To find the value of a $5,000 deposit at the end of 3 years with a 4% semi-annual compounded interest, we apply the compound interest formula to get approximately $5,630.81.
Step-by-step explanation:
You are considering investing $5,000 in a bank term deposit for 3 years. The term deposit will pay a semi-annual interest rate of 4%, compounded semi-annually. To calculate the value of the deposit at the end of year 3, we use the formula for compound interest:
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 or borrowed for, in years.
For this investment:
- P = $5,000
- r = 4% or 0.04 (as a decimal)
- n = 2 (since interest is compounded semi-annually)
- t = 3 years
We plug in these values to get:
A = $5,000(1 + 0.04/2)^(2*3)
A = $5,000(1 + 0.02)^(6)
A = $5,000(1.02)^6
A = $5,000 * 1.126162
A = $5,630.81 approximately
Therefore, the value of the deposit at the end of year 3 is approximately $5,630.81.