Question

Your client has accumulated some money for his retirement. He is going to withdraw $59,159 every year at the end of the year for the next 19 years. How much money has your client accumulated for his retirement? His account pays him 16.62 percent per year, compounded annually. To answer this question, you have to find the present value of these cash flows.

Round the answer to two decimal places.

Answer 1

To determine the retirement fund's accumulated amount, the present value of the annuity must be computed using the formula for the present value of an annuity with a 16.62% annual interest rate, and a 19-year term with annual payments of $59,159.

Step-by-step explanation:

To calculate how much money the client has accumulated for retirement, you must find the present value of the annuity that pays out $59,159 annually for 19 years with an interest rate of 16.62%, compounded annually. The formula for the present value of an annuity is given by:

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

Where:

• Pmt = annual payment amount
• r = annual interest rate (in decimal form)
• n = number of years

In this case:

• Pmt = $59,159
• r = 0.1662 (16.62%)
• n = 19

Plugging the values into the formula:

PV = $59,159 * [(1 - (1 + 0.1662)^(-19)) / 0.1662]

By calculating the above expression, we can find the present value that the client has accumulated for retirement.

Answer 2

To find the accumulated retirement money, given annual withdrawals of $59,159 at a 16.62% interest rate for 19 years, calculate the present value of the annuity using the specified formula. This will give the total amount of money the client has saved.

Step-by-step explanation:

To determine how much money your client has accumulated for retirement, assuming he withdraws $59,159 annually at a 16.62% annual interest rate, we need to calculate the present value of an annuity. This involves finding the sum of all withdrawals discounted back to their present value.

The formula for the present value of an annuity is PV = PMT × [(1 - (1 + r)²{-n}) / r], where PMT is the annual payment, r is the annual interest rate, and n is the number of years.

In this case, PMT = $59,159, r = 0.1662 (16.62%), and n = 19. Plugging these values into the formula gives us:

PV = $59,159 × [(1 - (1 + 0.1662)²{-19}) / 0.1662]

Calculating the above expression gives us the accumulated amount for retirement.