how do I solve the problem on a finance calculator.

Question

Suppose you need to have $50,113.00 in an account 22.00 years from today and that the account pays 11.00%. How much do you have to deposit into the account 12.00 years from today?

Answer 1

To solve this problem, we need to determine how much you need to deposit into an account 12 years from today in order to have $50,113.00 in that account 22 years from today, given that the account earns an annual interest rate of 11.00%.

Steps to solve the problem:

1. Determine the Future Value (FV):

   • You want to have \( FV = 50,113.00 \) in 22 years.

2. Calculate the Present Value (PV) of that Future Value 10 years from now (since you are making the deposit 12 years from today and it will grow for another 10 years).

   • The formula to calculate the Present Value \( PV \) at a given interest rate over a period of time for future value is: \[ PV = \frac{FV}{(1 + r)^n} \]
   • Where:
     • \( FV \) is the future value ($50,113.00)
     • \( r \) is the interest rate (11% or 0.11)
     • \( n \) is the number of years (10 years)

3. Plug in the numbers: \[ PV = \frac{50,113.00}{(1 + 0.11)^{10}} \] \[ PV = \frac{50,113.00}{(1.11)^{10}} \]

   • First calculate \( (1.11)^{10} \): \[ (1.11)^{10} \approx 2.8394 \quad \text{(using a calculator)} \]
   • Then calculate \( PV \): \[ PV = \frac{50,113.00}{2.8394} \approx 17,637.10 \]

4. Interpret the Present Value:

   • The amount you need to deposit 12 years from today in order to have $50,113.00 in 22 years at an interest rate of 11% is approximately $17,637.10.

Summary:

To have $50,113.00 in 22 years, you need to deposit approximately $17,637.10 in the account at 12 years from today.

Answer 2

What do i enter for N, i,y, PMT, PV and FV on a finance calculator

Answer 3

To solve the problem using a financial calculator, you'll need to input the following parameters into the respective fields:

Given Data:

1. Future Value (FV): $50,113.00 (the amount you want in the future)
2. Interest Rate (i): 11% (the annual interest rate)
3. Number of Years (N): 10 years (since you make the deposit 12 years from now and it has 10 more years to grow)
4. Payment (PMT): $0 (you are making a single deposit, not regular payments)
5. Present Value (PV): This will be computed based on your inputs, but you can leave it as 0 if your calculator requires it to be entered.

Financial Calculator Inputs:

• N: 10 (the number of years until you need the future value)
• i (Interest Rate): 11 (the annual interest rate)
• PV (Present Value): 0 (since you are calculating the future value from a single deposit)
• PMT (Payment): 0 (since there's no regular payment being made)
• FV (Future Value): 50,113 (the future value you want to achieve)

Steps to Calculate:

1. Input \( N = 10 \)
2. Input \( i = 11 \)
3. Input \( PMT = 0 \)
4. Input \( FV = 50,113 \)
5. Compute \( PV \) (the present value at which you need to make the deposit 12 years from today).

Expected Output:

After entering these values and computing for \( PV \), the calculator should display approximately $17,637.10. This is the amount you need to deposit 12 years from today in order to accumulate $50,113.00 in 22 years at an 11% annual interest rate.