Questions: Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have 100,000 after 18 years with an APR of 12% compounded quarterly. Round your answer to the nearest cent, if necessary.

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have 100,000 after 18 years with an APR of 12% compounded quarterly. Round your answer to the nearest cent, if necessary.

Transcript text: Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $100,000 after 18 years with an APR of 12% compounded quarterly. Round your answer to the nearest cent, if necessary.

Solution

Solution Steps

Step 1: Convert the Annual Percentage Rate (APR) to a decimal

To convert the APR from a percentage to a decimal, we divide the APR by 100. In this case, the APR of 12% becomes 0.12.

Step 2: Determine the compounding frequency

The compounding frequency is given as 4 times per year.

Step 3: Plug the values into the present value formula

We use the formula: \[ PV = \frac{FV}{(1 + \frac{r}{n})^{n_t}} \] Substituting the given values, we get: \[ PV = \frac{100000}{(1 + \frac{0.12}{4})^{4_18}} \]

Step 4: Calculate the present value

Using the values provided, the present value (PV) is calculated to be 11904.74.

Final Answer:

The amount that needs to be invested now to achieve the future value of $100000 in 18 years, given an annual interest rate of 12% compounded 4 times per year, is $11904.74.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!