Rick deposits$1000 into an investment account which earns 4% interest annually. Sally loans$1000 to a friend, and the friend agrees to pay her $50 each year, and will return the $1000 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
For Rick, the amount of money he will have after 10 years with a 4% interest rate annually can be calculated using the formula: A = P(1 + r/n)^(n*t), where A is the amount after time t, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years.
In this case, Rick's principal amount is $1000, the annual interest rate is 4% (or 0.04 as a decimal), and he has it compounded once per year. Plugging these values into the formula, we get:
A = 1000(1 + 0.04/1)^(1*10)
A = 1000(1 + 0.04)^10
A = 1000(1.04)^10
A ≈ $1,480.24
Therefore, Rick will have approximately $1,480.24 after 10 years.
For Sally, she loans $1000 to a friend who agrees to pay her $50 each year for 10 years and return the $1000 at the end. This means that Sally will receive $50 per year, with interest earned on the outstanding balance. The total amount she will receive can be calculated as:
Total amount = 50 * 10 + 1000
Total amount = $500 + $1000
Total amount = $1,500
Therefore, Sally will have $1,500 after 10 years.
The correct answer is D. Rick: $1,480.24; Sally $1,500