Please answer all questions and check if the ones with the answer already give are correct
Scenario 1: You would like to know how much you should place on deposit to have accumulated a certain amount of money by a specific future date. Scenario 2: You would like to know how much a given amount deposited today will grow into by a specific future date. Noah Ummm. I think scenario 1 is the situation that requires the calculation of a present value. The reason is that the amount to be placed on deposit is both and occurs Devin Very good! So here's your next question: How is the present value of a single amount calculated? Noah It can be calculated by rearranging the formula that is used in the calculation of a future value. To see this ... Devin Wait, wait, wait. Could you show me what you mean by writing it down? Here is a sheet of paper, show me how to rearrange the future value formula to solve for a present value. Noah OK, first, let's write down the equation used to calculate a future value (FV). The Calculation of a Future Value Future Value Present Value X Interest factor Next, let's rearrange the equation to isolate the present value (PV) term by dividing both sides of the equation by the interest factor Then, we'll simply rewrite the equation to put the unknown variable, the PV term, on the left-hand side of the equation: FV = PV X (1 + I)N 1 FV x PV (1 + IN 1 PV = FV X (1 + I)N So, does this make sense? We've rearranged the future value equation to solve for the present value. Also, notice that the present value interest factor is the of the future value interest factor. This means that you don't necessarily need two different interest factor tables for the single cash flow; you can make do using either simply the present value table or the future value table-so long as you use it correctly. Devin So, do you think that we're ready to do a problem? Noah Sure! Here's one from our homework. You work and I'll work, and we'll see if our answers match. Devin OK. Let's get started. Homework Problem Sarah wants to reduce the cost of graduate school by starting a savings plan today. As a sophomore, she has estimated that she has three years to accumulate the $22,500 that she needs to help cover some of her projected expenses. The account she would open would earn 8% per year compounded annually. So how much would she have to deposit today to accumulate $22,500 in three years? Or, stated differently, what is the value of $22,500? (Note: Round your answer to the nearest whole dollar.) $17,861 so that she would have the desired $22,500 I think that Sarah would have to deposit at the end of three years. Scenario 1: You would like to know how much you should place on deposit to have accumulated a certain amount of money by a specific future date. Scenario 2: You would like to know how much a given amount deposited today will grow into by a specific future date. Noah Ummm. I think scenario 1 is the situation that requires the calculation of a present value. The reason is that the amount to be placed on deposit is both and occurs Devin Very good! So here's your next question: How is the present value of a single amount calculated? Noah It can be calculated by rearranging the formula that is used in the calculation of a future value. To see this ... Devin Wait, wait, wait. Could you show me what you mean by writing it down? Here is a sheet of paper, show me how to rearrange the future value formula to solve for a present value. Noah OK, first, let's write down the equation used to calculate a future value (FV). The Calculation of a Future Value Future Value Present Value X Interest factor Next, let's rearrange the equation to isolate the present value (PV) term by dividing both sides of the equation by the interest factor Then, we'll simply rewrite the equation to put the unknown variable, the PV term, on the left-hand side of the equation: FV = PV X (1 + I)N 1 FV x PV (1 + IN 1 PV = FV X (1 + I)N So, does this make sense? We've rearranged the future value equation to solve for the present value. Also, notice that the present value interest factor is the of the future value interest factor. This means that you don't necessarily need two different interest factor tables for the single cash flow; you can make do using either simply the present value table or the future value table-so long as you use it correctly. Devin So, do you think that we're ready to do a problem? Noah Sure! Here's one from our homework. You work and I'll work, and we'll see if our answers match. Devin OK. Let's get started. Homework Problem Sarah wants to reduce the cost of graduate school by starting a savings plan today. As a sophomore, she has estimated that she has three years to accumulate the $22,500 that she needs to help cover some of her projected expenses. The account she would open would earn 8% per year compounded annually. So how much would she have to deposit today to accumulate $22,500 in three years? Or, stated differently, what is the value of $22,500? (Note: Round your answer to the nearest whole dollar.) $17,861 so that she would have the desired $22,500 I think that Sarah would have to deposit at the end of three years
