math homework 5 problems

One application of ‘Exponential Functions’ is the concept of compound interest.

In this case, we will use the following formula to determine the future value of an investment with monthly payments: A=Pleft[frac{left(1+rright)^n-1}{r}right]

A


=


P



[






(


1


+


r


)



n



−


1



r



]

.

A=future value P=payment amount r=interest rate per period n=number of payment periods

For example: If $100 were deposited monthly at annual interest rate of 12% for 20 years, then P = $100, r = .12/12 = .01 and n = 12*20 = 240. The formula would look like A = 100[(1+.01)^240-1]/0.1 = $98,925.54.

Write this formula down to use when answering the questions.

Question 1: Rachel deposits $200 into her retirement plan each month and her company also deposits half of Rachel’s monthly deposits into her retirement plan as well. Find the monthly total being deposited into Rachel’s retirement plan. The retirement plan earns 6% per year, compounded monthly, so the interest rate per period is 0.06/12 = 0.005. Rachel wants to retire in 30 years, so the number of monthly payments is 12 times 30 = 360. Using the formula stated in the instructions, how much money will Rachel have in her account when she wants to retire in 30 years? Round the answer to the nearest cent.

Question 2:How much money will Rachel have in her account if she decided to retire in 40 years in stead of 30 years? Round the answer to the nearest cent.

Question 3:How much more money would Rachel have by retiring in 40 years instead of 30 years? Round the answer to the nearest cent.

Question 4:How much money did Rachel and her company deposit into her account during the additional 10 years? Write the answer to the nearest whole dollar. Do not include any cents in the answer.

Question 5:How much extra money was in her account after 40 years as opposed to 30 years as a result of the compounded interest? Write the answer to the nearest cent.

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