Answer:
Joshua paid his friend 10% simple interest
Step-by-step explanation:
Simple Interest
Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.
The interest earned is calculated as follows:
I=P.r.t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
The final amount is calculated as:
A = P + I
A = P + Prt
A = P(1 + rt)
Joshua borrowed P=$1000 from his friend and paid him back A=$1050 in t=6 months = 6/12 = 0.5 years.
To find the annual interest rate, we solve for r:
[tex]\displaystyle r=\frac{A/P-1}{t}[/tex]
[tex]\displaystyle r=\frac{1050/1000-1}{0.5}[/tex]
[tex]\displaystyle r=\frac{1.05-1}{0.5}=0.1[/tex]
Converting to percentage
r = 0.1*100 = 10%
Joshua paid his friend 10% simple interest
