Rick deposits $1,000 into an investment account which earn4% interest 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 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
To determine the amount of money Rick has after 10 years with 4% annual interest rate, we use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (initial deposit or loan amount).
r is the annual interest rate (as a decimal).
n is the number of times the interest is compounded per year.
t is the number of years the money is invested or loaned for.
For Rick:
P = $1,000
r = 0.04
n = 1 (compounded annually)
t = 10
A = $1,000(1 + 0.04/1)^(1*10)
A = $1,000(1.04)^10
A = $1,000(1.48024459)
A = $1,480.24
So after 10 years, Rick will have $1,480.24.
For Sally:
Sally is paid $50 per year for 10 years by her friend, totaling $50/year * 10 years = $500
She also gets back her initial loan of $1,000 after 10 years.
So after 10 years, Sally will have $500 + $1,000 = $1,500.
Therefore, the correct answer is:
D) Rick $1,480.24; Sally: $1,500.