Another bank is also offering favorable terms, so Rahul decides to take a loan of $18,000 from this bank. He signs the loan contract at 10% compounded daily for three months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

Hi, in order to find the total amount that Rahul will owe the bank in 3 months, we need to use the following formula (this is for a compounded daily rate).

[tex]FutureValue=PresentValue(1+\frac{r}{365} )^{\frac{n*365}{12} }[/tex]

Where:

r = compounded rate (in our case, 10% compounded daily)

n = time in months of the loan

PresentValue = $18,000

Everything should look like this.

[tex]FutureValue=18,000(1+\frac{0.10}{365} )^{\frac{3*365}{12} }[/tex]

[tex]FutureValue=18,000(1+0.000273973 )^{91.25 }=18,455.61[/tex]

So, the total amount that Rahul owes the bank at the end of the loan's term is $18,455.61

Best of luck