drill problem 10-13 (algo) lu 10-3 (1) given principal $9,000, interest rate 6%, time 240 days (use ordinary…

Explanation:

Step1: Calculate interest before first - partial payment

The simple - interest formula under the U.S. Rule is $I = Prt$, where $P$ is the principal, $r$ is the interest rate, and $t$ is the time. For the first 100 days, $P=$9000$, $r = 0.06$, and $t=\frac{100}{360}$. $I_1=9000\times0.06\times\frac{100}{360}=$150$

Step2: Adjust principal after first - partial payment

After the first partial payment of $$3200$ on the 100th day, the new principal $P_1$ is $P_1=(9000 + 150)-3200=$5950$

Step3: Calculate interest from first - partial payment to second - partial payment

For the period from the 100th day to the 180th day ($t_2=\frac{180 - 100}{360}=\frac{80}{360}$), with $P_1 = 5950$ and $r = 0.06$ $I_2=5950\times0.06\times\frac{80}{360}\approx$79.33$

Step4: Adjust principal after second - partial payment

After the second partial payment of $$2200$ on the 180th day, the new principal $P_2$ is $P_2=(5950+79.33)-2200=$3829.33$

Step5: Calculate interest from second - partial payment to end of loan term

The remaining time $t_3=\frac{240 - 180}{360}=\frac{60}{360}$ $I_3=3829.33\times0.06\times\frac{60}{360}\approx$38.29$

Step6: Calculate total interest

The total interest $I = I_1+I_2+I_3$ $I=150 + 79.33+38.29=$267.62$

Answer:

$$267.62$