time value of money

this question involves calculating the future value (FV) of a series of equal annual deposits made into an investment account. You are given the following information:

• Annual deposit (PMT): $1,000
• Number of years (N): 10
• Interest rate (I/Y): Not explicitly provided, but you are given the future value (FV) of the investment after 10 years, which is $16,160.29.

The formula you will use for this calculation is the future value of an annuity formula:

��=���×((1+�)�−1�)FV=PMT×(r(1+r)n−1​)

Where:

• FV is the future value of the investment.
• PMT is the annual deposit.
• r is the annual interest rate.
• n is the number of years.

You need to solve for the annual interest rate (r) first, given that you have the FV and PMT:

16,160.29=1,000×((1+�)10−1�)16,160.29=1,000×(r(1+r)10−1​)

Now, to solve for r, you can use financial calculator functions. You are given the answer for this part, which is $16,160.29. Therefore, you need to set up your calculator as follows:

PMT = -1000 (negative because it’s an outgoing payment) N = 10 FV = 16,160.29 PV = 0 (initial investment) CPT I/Y (compute interest rate)

When you compute the interest rate (I/Y), you should get an annual interest rate of approximately 5.63%.

Now that you have the annual interest rate, you can calculate the future value after 20 years using the same formula:

��=���×((1+�)�−1�)FV=PMT×(r(1+r)n−1​)

Where:

• PMT = $1,000
• r = 5.63% (or 0.0563 as a decimal)
• n = 20 (20 years)

Plug these values into the formula:

��=1,000×((1+0.0563)20−10.0563)FV=1,000×(0.0563(1+0.0563)20−1​)

Now, calculate the future value:

��≈39,204.23FV≈39,204.23

So, after 20 years of making annual deposits of $1,000 into the investment account with an annual interest rate of 5.63%, you will have approximately $39,204.23. Therefore, the correct answer is:

B) $39,204