Chapter 9: Problem 18

Most spreadsheets have financial functions built in. Use these to answer the following question: If you now started saving $\$ 200$ per month until you were 65 , how much money would you have saved? Assume an annual interest rate of a) 4 percent, b) 6 percent, and c) 8 percent.

Short Answer

Expert verified

Answer: The future value of their savings at age 65 would be: a) 4% annual interest rate: $157,893.68 b) 6% annual interest rate: $230,528.25 c) 8% annual interest rate: $349,335.88

Step by step solution

Identify the variables in the problem

In this problem, the variables are: - Monthly payment (PMT) = $200 - Interest rates (annual) = [4%, 6%, 8%] - The period is until the person is 65 years old. We assume that the person starts saving today, so we need the current age of the person.

Calculate the number of months

Assuming the person is starting to save today, we need to calculate the number of months left until they reach the age of 65. Since this variable is missing, we could use either the current age of the student or another age to make our calculations. Let's assume that the person is currently 25 years old. Number of years left = 65 - 25 = 40 years Number of months left = 40 * 12 = 480 months

Iterate through the different annual interest rates

We will now make a loop for the three different interest rates: 4%, 6%, and 8%. In each iteration, we calculate the future value using the future value of an ordinary annuity formula.

Calculate the monthly interest rate

Divide the annual interest rate by 12 to obtain the monthly interest rate. Monthly interest rate = annual interest rate / 12

Apply the future value of an ordinary annuity formula

The formula for the future value of an ordinary annuity is given by: $FV = PMT \cdot (\frac{(1 + r)^{n} - 1}{r})$ Where: FV = Future value of the annuity PMT = Monthly payment r = Monthly interest rate n = Total number of months For each interest rate condition, plug in the values and compute the future value.

Calculate the future value for 4% annual interest rate

Monthly interest rate for 4% annual rate = (0.04) / 12 = 0.003333 Future value for 4% = 200 * ( ( (1 + 0.003333)^480 - 1 ) / 0.003333 ) = $\$157,893.68$

Calculate the future value for 6% annual interest rate

Monthly interest rate for 6% annual rate = (0.06) / 12 = 0.005 Future value for 6% = 200 * ( ( (1 + 0.005)^480 - 1 ) / 0.005 ) = $\$230,528.25$

Calculate the future value for 8% annual interest rate

Monthly interest rate for 8% annual rate = (0.08) / 12 = 0.006667 Future value for 8% = 200 * ( ( (1 + 0.006667)^480 - 1 ) / 0.006667 ) = $\$349,335.88$

Present the results

By saving $200$ per month until age 65 with the given interest rates, the future value of the savings would be: a) 4% annual interest rate: $157,893.68 b) 6% annual interest rate: $230,528.25 c) 8% annual interest rate: $349,335.88

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Most spreadsheets have financial functions built in. Use these to answer the following question: If you now started saving \(\$ 200\) per month until you were 65 , how much money would you have saved? Assume an annual interest rate of a) 4 percent, b) 6 percent, and c) 8 percent.

Short Answer

Step by step solution

Identify the variables in the problem

Calculate the number of months

Iterate through the different annual interest rates

Calculate the monthly interest rate

Apply the future value of an ordinary annuity formula

Calculate the future value for 4% annual interest rate

Calculate the future value for 6% annual interest rate

Calculate the future value for 8% annual interest rate

Present the results

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