Prob 1.1 Meliss part 2 1. Melissa needs some home repairs in five years that wil
ID: 2619632 • Letter: P
Question
Prob 1.1 Meliss part 2
1. Melissa needs some home repairs in five years that will cost $10,000. She has some money in an account earning 6% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs?
2. Unfortunately, Melissa doesn’t have enough money in her account right now. She needs to make additional contributions at the end of next five years to be able to pay for the repairs. Her account currently has $4,000, which, along with her additional contributions, is expected to continue earning 6% annual interest. If she makes equal contributions each year, how large much each contribution be for Melissa to have $10,000 after six years?
$7,472.58 [ 10000/1.06 5 ] amount need to be in account -Explanation / Answer
Step 1: Calculate Future Value of $4,000 at the End of 6 Years
The future value of a lump sum amount can be calculated as below:
Future Value of $4,000 after 6 Years = Amount*(1+Interest Rate)^6 = 4,000*(1+6%)^6 = $5,674.08
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Step 2: Calculate the Future Value of Annual Contributions at the End of 6 Years
The future value of annual contributions at the end of 6 years is arrived as below:
Future Value of Annual Contributions at the End of 6 Years = Total Amount Needed after 6 Years - Future Value of $4,000 after 6 Years = 10,000 - 5,674.08 = $4,325.92
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Step 3: Calculate Present Value of $4,325.92 at the End of 5 Years
The present value of $4,325.92 at the end of 5 years is calculated as below:
Present Value of $4,325.92 at the End of 5 Years = 4,325.92/(1+6%)^1 = $4,081.06
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Step 4: Calculate the Amount of Equal Contribution to Made for Next 5 Years
The amount of equal contribution can be calculated with the use of PMT (Payment) function/formula of EXCEL/Financial Calculator. The function/formula for PMT is PMT(Rate,Nper,PV,FV) where Rate = Interest Rate, Nper = Period, PV = Present Value and FV = Future Value.
Here, Rate = 6%, Nper = 5, PV = 0 and FV = 4,081.06
Using these values in the above function/formula for PMT, we get,
Amount of Equal Contribution = PMT(6%,5,0,4081.06) = $723.96 (answer)
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Notes:
1) There can be a slight difference in final answer on account of rounding off values.
2) It has been assumed that the total number of payments will be 5 starting from end of Year 1. However, the amount is required after 6 years from the first annual contribution.
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