Calculate Annual Interest Rate for Deposits

A

On the BAII Plus, press 20 N, 0 PV, 1000 PMT, 40000 +/- FV, CPT I/Y. On the HP12C, press 20 n, 0 PV, 1000 PMT, 40000 CHS FV, i. Make sure that the BAII

Plus has the P/Y value set to 1.

To find the annual interest rate that would cause a series of 20 deposits of $1,000 to accumulate to $40,000, we can use the concept of future value and the formula for compound interest.

The formula for future value (FV) of a series of deposits with compound interest is:

FV = P * ((1 + r)^n - 1) / r

Where: FV = Future value P = Periodic deposit (in this case, $1,000) r = Annual interest rate (compounded annually) n = Number of deposits (in this case, 20)

We know that the future value (FV) is $40,000, the periodic deposit (P) is $1,000, and the number of deposits (n) is 20. We need to solve for the annual interest rate (r).

The equation becomes:

$40,000 = $1,000 * ((1 + r)^20 - 1) / r

To solve this equation, we can use a financial calculator or an equation solver. However, since we don't have that capability in this text-based format, we'll use an iterative approach to find the answer.

We'll start by plugging in one of the answer choices and see if it gives us a future value close to $40,000. Let's start with answer choice A: 6.77%.

r = 0.0677 (6.77% expressed as a decimal)

$40,000 = $1,000 * ((1 + 0.0677)^20 - 1) / 0.0677

Simplifying the equation:

$40,000 = $1,000 * (1.0677^20 - 1) / 0.0677

Calculating 1.0677^20 using a calculator, we get approximately 2.2086.

$40,000 = $1,000 * (2.2086 - 1) / 0.0677

$40,000 = $1,000 * (1.2086) / 0.0677

$40,000 ≈ $17,862.63

The future value using an interest rate of 6.77% is not close to $40,000.

Now, we'll repeat the process with the remaining answer choices.

Using answer choice B: 8.03% (0.0803 as a decimal):

$40,000 = $1,000 * ((1 + 0.0803)^20 - 1) / 0.0803

Calculating 1.0803^20 using a calculator, we get approximately 2.1917.