Upon graduation from​ college, Warren Roberge was able to defer payment on his ​$22,000 student loan for 3 months. Since the interest will no longer be paid on his​ behalf, it will be added to the principal until payments begin. If the interest is 6.94 ​% compounded monthly ​, what will the principal amount be when he must begin repaying his​ loan?

Answer:The principal amount be when he must begin repaying his​ loan is $22383.911.Step-by-step explanation: Given : Upon graduation from​ college, Warren Roberge was able to defer payment on his ​$22,000 student loan for 3 months. If the interest is 6.94 ​% compounded monthly.To find : What will the principal amount be when he must begin repaying his​ loan?Solution : Using compound interest formula,[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, A is the amount P is the principal P=$22,000r is the rate r=6.94%=0.0694t is the time t=3 months Into years, [tex]t=\frac{3}{12}=\frac{1}{4}[/tex]n is the number of period n=12Substitute the value in the formula,[tex]A=22000(1+\frac{0.0694}{12})^{12\times \frac{1}{4}}[/tex][tex]A=22000(1+0.005783)^{3}[/tex][tex]A=22000(1.005783)^{3}[/tex][tex]A=22000(1.01745)[/tex][tex]A=22383.911[/tex]The principal amount be when he must begin repaying his​ loan is $22383.911.