Problem Set 1

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University of Maryland Global Campus (UMGC) *

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105

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Economics

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Feb 20, 2024

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docx

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Percentage of Decrease and Increase; Unit Prices; Proportions Use the information in the chart below corresponding to your assigned number to answer the three questions. Show all your steps to reach your answers. You go to your favorite food market and see an item that you used to regularly purchased, although the last time was 8 months ago. 1. The package looks the same BUT looking at the label you see that the number of pieces in the package has decreased. What was the percentage of decrease in the quantity? Round answer to one decimal place. 2. Use a proportion to determine what the new selling price should be with this reduction in quantity. 3. Rather than a reduced price because the quantity was reduced, the price is kept the same as the original price. So, the price of each piece in the new package will have increased. a. Find the price of each piece (ie the unit price) in the original package and in the new package. b. Then determine the percentage of price increase for each piece. Round answer to one decimal place.

Assigne d Number Original Packag e: Numbe r of items New Package: Number of items Price of original package 9 232 pieces 200 pieces $4.00 1. 232-200= 32 32/232= 0.13793103448275862068965517241379 0.13793103448275862068965517241379 x 100 = 13.793103448275862068965517241379 Rounded answer: 13.8% 2. 4/232 = x/200 Reduce to 1/58 = x/200 Multiple by 200 to isolate x 200(1/58) = 200(x/200) 200/58 = x X= $3.45 New selling price should be $3.45 3a. Original packaging: $4/232 = $0.01724137931034482758620689655172 New Packaging: $4/200 = $.02 3b. [(0.02 - 0.01724137931034482758620689655172)/ .01724137931034482758620689655172] x100 [.00275862068965517241379310344828/.01724137931034482758620689655172] x100 0.16000000000000000000000000000028 x100 16% increase

Problem Set 2 Assigned # Amount Invested Annual Interest Rate # times per years interest is calculated 9. $4000 4.4% Weekly 1. Find the amount in the compound interest account after two years, assuming no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest cent. 2. Find the effective annual interest rate, expressed as a percentage. Do not round any intermediate computations, and round your answer to the nearest hundredth of a percent. 1. x= 4000(1 + .044/52)^(52x2) x= 4000(1 + 0.00084615384615385 )^104 x = 4000 x 1 .00084615384615385^104 x=4000 x 1.0919474901457403493824620562494 x= 4,367.7899605829613975298482249974 Account balance: $4,367.79 2. x= (1+0.04452)^52 −1 x= (1+0.04452)^52 −1 x= 0.044963 Effective annual interest rate: 4.50

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Set 2 #2 Instructions Question 2 Mortgage Loan Use the information in the chart below on the line that corresponds to your assigned number, to answer the following questions. Be sure to show all the steps you took to reach your answers. 1. What will your monthly mortgage payment be? Do not round any intermediate computations, and round your answer to the nearest cent. 2. Assuming you take the full term of the mortgage, how much total interest will you have paid? Do not round any intermediate computations, and round your answer to the nearest cent. Assigned # Price of the House Mortgage Interest Rate Term of Mortgage 9 $300,000 5.6% 15 years 1.

R = 300,000 (0.056/12) --------------------------- 1- (1+ 0.056/12)^-12(15) Calculator key strokes: ( 300000 ( .056/ 12 ) ) / ( 1- ( 1+ .056 / 12 ) ^ ( 12 ( 15 ) ) Rounded Answer: $2,467.20 2. 2,467.20 *12*15= 444,096.000 (total repayment amount) 444,096- 300,000= $144,096.00 total interest

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