ii. a $5000 loan at 6.8% was made on march 1. two payments of $2000 each were made on may 1 and june 1. what…

Explanation:

Step1: Calculate interest from March 1 - May 1 (2 months)

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Here, $P=$5000$, $r = 0.068$, and $t=\frac{2}{12}$. $I_1=5000\times0.068\times\frac{2}{12}=\frac{5000\times0.068\times2}{12}=\frac{680}{12}\approx$56.67$ The balance after two months is $P_1 = 5000 + 56.67=5056.67$. After the first payment of $$2000$ on May 1, the balance is $P_{2}=5056.67 - 2000=$3056.67$.

Step2: Calculate interest from May 1 - June 1 (1 month)

Using the simple - interest formula with $P = 3056.67$, $r = 0.068$, and $t=\frac{1}{12}$. $I_2=3056.67\times0.068\times\frac{1}{12}=\frac{3056.67\times0.068}{12}\approx$17.31$ The balance after this interest is added is $P_3 = 3056.67+17.31 = 3073.98$. After the second payment of $$2000$ on June 1, the balance is $P_{4}=3073.98 - 2000=$1073.98$.

Step3: Calculate interest from June 1 - August 1 (2 months)

Using the simple - interest formula with $P = 1073.98$, $r = 0.068$, and $t=\frac{2}{12}$. $I_3=1073.98\times0.068\times\frac{2}{12}=\frac{1073.98\times0.068\times2}{12}\approx$12.13$ The final payment on August 1 to pay off the loan is $P_5=1073.98 + 12.13=$1086.11$.

Answer:

$$1086.11$