Answer:
Step-by-step explanation:
We are told that Brenda wants to have $15,000 in 8 years and her money will earn 5% compound interest annually.
We need to figure out how much she should deposit now. We'll call that amount the present value (PV).
The formula for present value is:
Where:
- FV is the future value, or the amount she wants in 8 years ($15,000)
- r is the interest rate (0.05 or 5% expressed as a decimal)
- t is the number of time periods (8 years)
Plugging in the values:
PV = 15,000 / (1 + 0.05)^8
PV = 15,000 / 1.493
PV = $10,064
So Brenda should deposit $10,064 now in order to have $15,000 in 8 years, assuming a 5% annual compound interest rate.
The formula works because the $10,064 will grow to $15,000 over 8 years at 5% interest, compounded annually.
The key steps are:
- Determining the present value formula
- Identifying the given values: future value, interest rate, number of years
- Plugging those values into the formula
- Calculating the present value amount Brenda should deposit