Question

Chelsea's cousin needs to borrow money again. This time Chelsea loansher $500 at 4% interest compounded quarterly. The cousin pays her backagain in six months. What is the total amount the cousin owes Chelsea?

Answer 1

For an amount whose interest is compounded quarterly, the formula applied is;

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \text{Where;} \\ P=500,r=0.04,n=4,t=1 \end{gathered}`

Since the cousin pays back in 6 months, then the value of t, which is time, shall be 0.5. Hence, we would have;

`\begin{gathered} A=500(1+(0.04)/(4))^(4*0.5) \\ A=500(1+0.01)^2 \\ A=500(1.01)^2 \\ A=500*1.0201 \\ A=510.05 \end{gathered}`

The total amount the cousin owes Chelsea is $510.05