what do I enter for N, PMT, PV,FV, and i/y to solve on a finance calculator for the question below.

Question

Derek can deposit $267.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 14.00% and compounds interest monthly. Derek can deposit $2,552.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?

Answer 1

To solve for the equivalent interest rate at Bank B, we need to first calculate the future value (FV) of Derek's investment in Bank A, and then use that FV to determine the necessary interest rate for the account at Bank B.

Step 1: Calculate Future Value at Bank A

Bank A Details:

• PMT (Monthly Deposit) = $267
• i/y (Monthly Interest Rate) = 14% annual rate / 12 months = 1.1667% per month
• N (Total Periods) = 10 years * 12 months/year = 120 months
• PV (Present Value) = $0 (since this is a new account)

Now, we can input these values into a financial calculator or use the future value formula for annuities.

• N = 120
• PMT = 267
• PV = 0
• i/y = 14% / 12 = 1.16667 (rounded)
• FV = ?

Using these values in a financial calculator, you would solve for FV.

Step 2: Calculate the FV for Bank A

Using the future value annuity formula: \[ FV = PMT \times \left( \frac{(1 + i)^N - 1}{i} \right) \]

Substituting in the values: \[ FV = 267 \times \left( \frac{(1 + 0.0116667)^{120} - 1}{0.0116667} \right) \] Calculating this gives the future value of Derek’s account in Bank A.

Step 3: Setup Bank B Calculation

Bank B Details:

• PMT (Annual Deposit) = $2,552
• N (Total Periods) = 10 years
• PV = 0 (since this is also a new account)
• FV = Future Value calculated from Bank A.
• i/y = Required interest rate (to be determined).

Now, you can use the future value formula for Bank B.

Future Value for Bank B:

The formula is similar, but because it compounds annually: \[ FV = PMT \times \left( \frac{(1 + r)^N - 1}{r} \right) \]

Where \( r \) is the interest rate we want to determine. You will input \( FV \) from Bank A, \( PMT = 2552 \), and \( N = 10 \) into the financial calculator and solve for \( i/y \).

Summary of Entries for the Financial Calculator:

For Bank A:

• N = 120
• PMT = 267
• PV = 0
• i/y = 1.16667
• FV = (to be calculated)

For Bank B:

• N = 10
• PMT = 2552
• PV = 0
• FV = (the value obtained from Bank A calculation)
• i/y = (to be solved for rate)

You can use the FV you calculated from Bank A's future value to find the rate \( i/y \) at Bank B required to match that amount.