Question

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

Answer 1

My choice is C

Answer 2

let's first see what happens with Sally's bucks...

Answer 3

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
\(\large\color{#000000 }{ \displaystyle =1000+50\times 10 =1500 }\)

Answer 4

So we can exclude C.

Answer 5

Now, let's go ahead and analyze Rick's financial situation.

Answer 6

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

Answer 7

That's $1,400 @SolomonZelman