Math-144
December 8, 2015
Professor
Mission Project B
On This mission trip we are heading to Viedma Argentina. There will be 10 people going including myself and we will stay for a total of 4 weeks. The purpose of our mission trip is to bring supplies to the poor people of this country. The reason I chose Argentina is because of its economic issues in regards to there being so many people living in poverty (Reed, D. 2014). The supplies we will be bringing will be all donated items from churches and from different companies. This includes clothes, food, toys, pampers, toiletries, school supplies, household items (pots, dishes etc), and linens. These supplies will be sent over ahead of time eliminating us having to bring it ourselves. I will break down the total amount of expenses needed to cover this trip to make sure we are on budget and covered in every aspect.
A flight to Viedma Argentina costs $3,185.60 per person round trip from May 16th until June 13th, I found this price on the Priceline website. For ten people this will cost $31,856. The flight will take 25 hours and 19 minutes from Savannah, Ga to Viedma because there will be 3 different layover stops. For our lodging instead of booking a hotel I chose to find a vacation rental because hotels don’t have kitchens in the rooms and room service will eventually be more costly. The home, Casa balneario el condor Viedma costs $130 per night instead of per person, per night at the hotels. For the duration of 27 nights the total cost would come up to $3,510 plus an extra $100 as a security payment and $211 for service fees. This will bring the total cost of lodging to $3,821 (Houses for Rent in Balneario El Cóndor, n.d.).
As far as our supplies are concerned, it will cost us $373.57 per 100lb box and it will take about 20 days for the packages to get there. We plan on sending 30 boxes at a total cost of $11,207.10 via shipnex a worldwide shipping company (Nex Worldwide Express, nd). Other expenses such as passports and other documents will cost $165.00 (U.S. Passports & International Travel, 2015). The amount we will need for food would be $1,000. For our transportation the mission we will be working with in Argentina has a van they will be loaning us for the duration of our stay. We will bring $300 for gas with us just in case. Lastly our medical expenses will be covered by The International Medical Group (IMG) at total $700 with a $0 deductible and that will keep us covered for the 28 days we will be out there. The entire cost of this trip will cost us a total of $49,049.10. Once in the country we will have to exchange our currency for Argentine pesos. $1.00 USD is equivalent to $9.73 in AP (Argentine pesos) which we will have to exchange $5,821 in USD to get back $56,561.78 AP. This money will cover the in-country expenses such as Transportation ($300=$2915.06 gas), Food ($1,000=$9,716.85), Lodging ($3,821=$37,128.08), and Medical insurance ($700=$6801.80)
To pay for this trip we have a bank account already set up where we will keep adding to it throughout the next 5 years. Our initial investment for this mission will be the 10% that we already have which is $4,904.91. We will be investing the money at a 4% APR compounded quarterly. Using the compound formula from p. 216 of our textbook this is how the numbers figured out quarterly (Bennett, J., & Briggs, W. 1999. Pg.216).
At=A01+rNN⋅t
Here A(t)= value of account after t years (the final answer), A0 =the initial investment ($4,904.91), r = APR (0.04), N = number of times compounded quarterly, t = number of year (5).
Quarterly
What I did was divide the 0.04 by 4 which gave me 0.01. I add the one to that and now have 1.01. I raise that to the 4*5= 20th power which would give me 1.22019003995. I finally multiply this number and 4,904.91 together and was left with $5984.92.
At=A01+rNN⋅t

At=$4,904.911+0.0444⋅5=$5,984.92

An alternative way to help pay for the trip is having Missions R Us agree to give our group $100.00 every month from now until the time our trip begins. This money will be placed in an account that earns 6% APR compounded monthly. This will amount to $6,977.00 by the time the trip starts.
A(t)=PMT⋅1+rNN⋅t-1rN

A(t)=100⋅1+0.06%1212⋅5-10.06%12
First I simplify the top portion by dividing the 0.06 into 12 which gives me 0.005 and I add the 1 which now gives me 1.005. I multiplied the 12*5 exponents which gave me 60, then I took the 1.005 and raised it to the 60th power leaving me with 1.34885015255. I subtract 1 from that number leaving me with 0.34885015255. I finally take that number and multiply it to 100 which equals 34.88501525493. I now divide that number by 0.005 which leaves me with 6,977.00
A(t)=100*0.34885015255=34.885015254930.06%12=0.005

A(t)=34.885015254930.005
34.88501525493 ÷ 0.005 = 6,977.00
With the 10% we originally started with which was the $5,984.92 and the money donated from Missions R Us which was $6,977.00, combined we have a total of $12,961.92. To find out how much money is still needed for this trip I will subtract the $12,961.92 from the original cost of the trip which is $49,049.10 thus leaving me with a total of $36,087.18 left unpaid for. In order to make the rest of this money we would have to now take out a loan from a bank. Bank A is willing to lend us a 5 year loan at a 9% APR compounded monthly with monthly payments. Bank B is willing to lend us a 10 year loan at a 12% APR compounded monthly with monthly payments as well.

Bank A
PMT=P⋅rN1-1+rN-N⋅t
Bank A: Here P= the initial loan amount ($36,087.18), r= annual interest rate as a decimal (0.09%), N= number of times compounded monthly (12), t= time of the loan in years (5), PMT= monthly payment.

PMT=36,087.18⋅0.09%121-1+0.0912-12⋅5

First I simplify the top portion by taking the 0.09 and dividing it by 12 which gives me 0.0075. I then take that 0.0075 and multiply it by the $36,087.18 which leaves me with 270.65385

PMT=36,087.18⋅0.0075=270.653851-1+0.0912-12⋅5

Then I simplify the bottom portion by dividing the 0.09 by 12 which leaves me with 0.0075. I then add 1 to that number which gave me 1.0075. I took the exponents -12 and multiplied it by 5 which gave me -60. I raised the 1.0075 to the -60th power and got 0.63869969859. I then subtracted 1 from that and was left with -0.36130030141.

PMT=270.65385-0.36130030141= -$749.11

I divide the -0.36130030141 by the 270.65385 and I am left with a monthly payment of -$749.11.

Bank B

PMT=P⋅rN1-1+rN-N⋅t
Bank B: Here P= the initial loan amount ($36,087.18), r= annual interest rate as a decimal (0.12%), N= number of times compounded monthly (12), t= time of the loan in years (10), PMT= our monthly payment.

PMT=36,087.18⋅0.12%121-1+0.1212-12⋅10

First I simplify the top portion by taking the 0.12 and dividing it by 12 which gives me 0.01. I then take that 0.01 and multiply it by the $36,087.18 which leaves me with 360.8718.

PMT=36,087.18⋅ 0.01=360.87181-1+0.1212-12⋅10=

Then I simplify the bottom portion by dividing the 0.12 by 12 which leaves me with 0.01. I then add 1 to that number which gave me 1.01. I took the exponents -12 and multiplied it by 10 which gave me -120. I raised the 1.01 to the -120th power and got 0.30299477969. I then subtracted 1 from that and was left with -0.69700522031.

PMT=360.8718-0.69700522031= -$517.75

I divide the -0.697005220310 by the 360.8718 and got -$517.74619398044 which I rounded to the nearest cent and I am left with a monthly payment of -$517.75

Mission Budget Sheet

The total on the screen shot above could not be changed from what was already written but the real total is $49,049.10. I kept getting that message so I screen shot it so you know why I could not do it correctly.

Reference list
Bennett, J., & Briggs, W. (1999). Using and understanding mathematics: A quantitative reasoning approach. Reading, MA: Addison-Wesley.
Casa balneario El Condor Viedma - Houses for Rent in Balneario El Cóndor. (n.d.). Retrieved December 13, 2015, from https://www.airbnb.com/rooms/828998?checkin=05/17/2016&checkout=06/13/2016&guests=7&s=z_Adi2Ou
Fees. (2015, July 29). Retrieved December 13, 2015, from http://travel.state.gov/content/passports/en/passports/information/fees.html
Nex Worldwide Express - The Safer, Easier way to Ship. (n.d.). Retrieved December 13, 2015, from https://www.shipnex.com/express-shipping-rates.aspx?type=int&SenderCountry=447&SenderCityZip=31419&ReceiverCountry=255&ReceiverCityZip=viedma&Weight=100#getQuickQuote
Reed, D. (2014, July 3). Retrieved December 13, 2015, from http://www.theguardian.com/cities/2014/jul/03/buenos-aires-poor-fight-survive-wealthy-shop-argentina-inequality