Question

Future value = p × (1 i)t present value = kate wants to have $25,000 in 16 years. how much does she need to invest if the interest rate is 6 percent per year?

Option 1: $10,431.63
Option 2: $9,841.16
Option 3: $7,353.88
Option 4: $12,000.00

Answer 1

Using the present value formula, Kate would need to invest approximately $8,754.47 today at a 6% annual interest rate to have $25,000 in 16 years. The options provided do not match this calculation.

Step-by-step explanation:

To calculate the amount Kate needs to invest to have $25,000 in 16 years with an interest rate of 6% per year, we use the present value formula:

PV = FV / (1 + i)t

Where:

• PV is the present value (how much to invest now)
• FV is the future value (the amount wanted in the future, which is $25,000)
• i is the interest rate (0.06 for 6%)
• t is the number of years (16 years)

Plugging in the values, we get:

PV = $25,000 / (1 + 0.06)16

PV = $25,000 / (1.06)16

PV = $25,000 / 2.8569

PV = $8,754.47 (approx)

Therefore, this calculation suggests that none of the given options are entirely accurate. Kate would need to invest approximately $8,754.47 today to have $25,000 in 16 years, assuming a 6% annual interest rate.