ane Frost wants to receive yearly payments of $20,000 for 12 years. How much must she deposit at her bank today at 12% interest compounded annually? (Do not round intermediate calculations. Round your answer to the nearest cent.)

To solve this problem, we need to use the formula for the present value of an annuity. The formula is:

PV = PMT * [(1 - (1 + r)^-n) / r]

where:

• PV is the present value, or the amount that needs to be deposited today.
• PMT is the annual payment, which is $20,000.
• r is the annual interest rate, which is 12% or 0.12.
• n is the number of years, which is 12.

Substituting the given values into the formula, we get:

PV = $20,000 * [(1 - (1 + 0.12)^-12) / 0.12]

Now, we can calculate the present value.

First, calculate the value of (1 + r), which is (1 + 0.12) = 1.12.

Next, raise this value to the power of -n, which is -12. So, (1.12)^-12 = 0.32197.

Subtract this value from 1, which gives (1 - 0.32197) = 0.67803.

Finally, divide this value by r, which is 0.12, and multiply by PMT, which is $20,000. So, PV =$20,000 * (0.67803 / 0.12) = $113,002.50.

So, Jane Frost must deposit $113,002.50 in her bank today to receive yearly payments of$20,000 for 12 years at an interest rate of 12% compounded annually.