anonymous
  • anonymous
Can someone check this? Rick deposits $1,000 into an investment account which earns 4% annually. Sally loans $1,000 to a friend, and the friend agrees to pay her $50 each year, and will return the $1,000 after 10 years. Determine the amount of money each person has after 10 years A. Rick: $1,040; Sally: $1,500 B. Rick: $1,453.16; Sally: $1,500 C. Rick: $1,534.32; Sally: $2,000 D. Rick: $1,480.24; Sally: $1,500
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
My choice is C
SolomonZelman
  • SolomonZelman
let's first see what happens with Sally's bucks...
SolomonZelman
  • SolomonZelman
Sally's friend agrees to pay $50 each year, and since the friend will return the $1000 after 10 years we can imply that he will have been paying $50 annually during a 10-year period. So sally gets her initial money (=1000), and ten times of $50 yearly payments (=10•50=500). So overall sally is going to have \(\large\color{#000000 }{ \displaystyle =1000+50\times 10 =1500 }\)

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SolomonZelman
  • SolomonZelman
So we can exclude C.
SolomonZelman
  • SolomonZelman
Now, let's go ahead and analyze Rick's financial situation.
SolomonZelman
  • SolomonZelman
Rick had invested $1000 (this 100% of his money) And, he is getting 4% more every year. After 1 year he has additional 4%. After 2 year he has additional (4•2)%. After 3 year he has additional (4•3)%. \(\bf ....\) After 10 year he has additional (4•10)% \(\Longrightarrow\) additional 40%. \(\color{#0000ff}{\Huge ^{^\text{__________________________________________}}}\) Keep in mind that he still owns/has 100% (the initial $1000 investment) And altogether, that is 140% (of/from $1000) \(\color{#0000ff}{\Huge ^{^\text{__________________________________________}}}\) So all you need to do is to find 140% of 1000. (Note: 140% of 1000 = (140/100)•1000 which can be also be re-written as follows; 140•(1000/100) ~~SZ
anonymous
  • anonymous
That's $1,400 @SolomonZelman

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