"Legitimate Financial Services made a loan at 9.75% interest for 254 days. If the amount of interest was $270.50, use the exact interest method to find the amount of principal borrowed. (Round to the nearest whole dollar amount)"

$3,979.

Explanation:

Interest can be described as the cost of borrowing. This means that the amount that is paid for using money borrowed from a bank or other financial institutions is called interest.

Interest can be ordinary interest or exact interest. When the estimation of an interest is done on the basis of of a 360-day year, it is called ordinary interest. But when the estimation of an interest is done on the basis of of a 365-day year, it is called exact interest.

The formula for calculating both ordinary and exact interests is the same, but it just the days has to be adjusted. The general formula is given as follows:

I = Prt (1)

Where,

P = principal borrowed = ?

r = interest rate = 9.75% = 0.0975

t = time expressed in years = 254

Equation (1) can be therefore be amended for days for ordinary interest as follows:

OI = Pr (D/360) (2)

Where

OI = ordinary interest

D = number of days = 254

D/360 = t for ordinary interest

Equation (1) can also be be amended for days for exact interest as follows:

OI = Pr (D/365) (3)

Where

OI = ordinary interest = $270

D = number of days = 254

D/365 = t for exact interest

Since the asked to use the exact method, we therefore use equation (3), substitute all the relevant value into it and solve for P as follows:

270 = P × 0.0975 × (254 ÷ 365)

270 = P × 0.0975 × 0.695890410958904  

270 = P × 0.0975 × 0.695890410958904

270 = P × 0.0678493150684931  

P = 270 ÷ 0.0678493150684931

P =  3,979.4064203513  

P = $3,979 (rounded to the nearest whole dollar amount)

Therefore, the amount of principal borrowed is $3,979.

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