Question

Rosalie wants to have $7,500 in 18 years. Use the present value formula to calculate how much Rosalie should invest now at 8% interest, compounded annually in order to achieve her goal.

Answer 1

Rosalie should invest approximately $1,877.72 today to have $7,500 in 18 years at an 8% interest rate, compounded annually, based on the present value calculation.

Step-by-step explanation:

The student's question is about present value in the context of financial mathematics. To achieve the goal of having $7,500 in 18 years with an 8% interest rate compounded annually, Rosalie must calculate the present value of this future amount.

Using the present value formula: PV = FV / (1 + r)ⁿ,

• PV represents the present value we aim to find.
• FV is the future value which is $7,500.
• r is the annual interest rate in decimal form, so 8% will be 0.08.
• n is the number of periods, in this case, 18 years.

We can now calculate the amount Rosalie needs to invest:

PV = $7,500 / (1 + 0.08)¹⁸

PV = $7,500 / (1.08)¹⁸

PV = $7,500 / 3.9960

PV = $1,877.72 approximately

Hence, Rosalie should invest approximately $1,877.72 today.

Answer 2

PV= $1,876.87

Step-by-step explanation:

Giving the following information:

Rosalie wants to have $7,500 in 18 years. Use the present value formula to calculate how much Rosalie should invest now at 8% interest.

We need to use the following formula:

PV= FV/(1+i)^n

PV= 7,500/(1.08^18)= $1,876.87