Answer :
Explanation :
simple interest is given by,
wherein,
here,
plugging in,
thus, her friend lent her money at an interest rate of 6% .
Answer:
6%
Step-by-step explanation:
We are told that Amrita borrowed $16,000 from a friend, and after 4 years, she paid back $19,840 to her.
To find the rate of interest charged by Amrita's friend, we can assume it was simple interest, as there is no mention of the type of interest, and therefore we use the simple interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Simple Interest Formula}}\\\\A = P(1 + rt)\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$A$ is the final amount.}\\ \phantom{ww}\bullet\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\\ \end{array}}[/tex]
In this case:
Substitute the values into the formula and solve for r:
[tex]19840=16000(1+r \cdot 4)\\\\\\19840=16000(1+4r)\\\\\\\dfrac{19840}{16000}=1+4r\\\\\\1+4r=1.24\\\\\\4r=1.24-1\\\\\\4r=0.24\\\\\\r=\dfrac{0.24}{4}\\\\\\r=0.06[/tex]
To convert the rate (r) into a percentage, multiply by 100:
[tex]r=0.06 \times 100\\\\\\r=6\%[/tex]
Therefore, the rate of interest charged by Amrita's friend was:
[tex]\LARGE\boxed{\boxed{6\%}}[/tex]
