Question

You want to have $87,000 in 16 years to help your child attend college. If you can earn an annual interest rate of 4.3 percent, how much will you have to deposit today? Multiple Choice

A)$23,588.79
B)$39,253.27
C)$42,529.08
D)$41,090.24
E)$44,357.83

Answer 1

To have $87,000 in 16 years with an annual interest rate of 4.3 percent, you would need to deposit (d) $41,090.24 today.

Step-by-step explanation:

This calculation is based on the future value formula for compound interest. The present value, or the initial deposit required today, is determined by discounting the future value back to the present using the interest rate. In this case, $41,090.24 is the amount you need to invest now to accumulate $87,000 after 16 years with an annual interest rate of 4.3 percent.

Investing involves the concept of the time value of money, where the purchasing power of money changes over time due to inflation or interest. By making an informed decision on the initial deposit, you can plan for future financial goals such as funding your child's college education.

Answer 2

To find out how much you need to deposit today to have $87,000 in 16 years at an annual interest rate of 4.3 percent, you calculate the present value using the formula PV = FV / (1 + r)^n, which results in a deposit of approximately $42,529.08. Thus (option C) is right answer.

Step-by-step explanation:

The question involves determining the present value of a future amount of money using the formula for compound interest. To find out how much you need to deposit today to have $87,000 in 16 years with an annual interest rate of 4.3 percent, you use the formula for the present value (PV) of a future amount:

PV = FV / (1 + r)n

where:

PV is the present value (what you need to deposit today)

FV is the future value ($87,000)

r is the annual interest rate (4.3% or 0.043)

n is the number of years (16)

By substituting the given values into the formula, the calculation becomes:

PV = $87,000 / (1 + 0.043)16

Using a calculator, we find that the present value is approximately $42,529.08, which matches choice C from the multiple-choice options provided.