diane took out a loan for 5 months and was charged simple interest at an annual rate of 4.8%. the total…

diane took out a loan for 5 months and was charged simple interest at an annual rate of 4.8%. the total interest she paid on the loan was $170. how much money did diane borrow? do not round any intermediate computations. if necessary, refer to the list of financial formulas.

diane took out a loan for 5 months and was charged simple interest at an annual rate of 4.8%. the total interest she paid on the loan was $170. how much money did diane borrow? do not round any intermediate computations. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Convert time to years

The loan is for 5 months. Since there are 12 months in a year, $t=\frac{5}{12}$ years. The annual interest rate $r = 4.8%=0.048$, and the interest $I = 170$. The simple - interest formula is $I=P\times r\times t$, where $P$ is the principal (the amount borrowed).

Step2: Solve for the principal $P$

We can re - arrange the simple - interest formula $I = P\times r\times t$ to solve for $P$. So $P=\frac{I}{r\times t}$. Substitute $I = 170$, $r=0.048$, and $t=\frac{5}{12}$ into the formula. $P=\frac{170}{0.048\times\frac{5}{12}}$ First, calculate $0.048\times\frac{5}{12}=0.048\times\frac{5}{12}=\frac{0.048\times5}{12}=\frac{0.24}{12}=0.02$. Then, $P=\frac{170}{0.02}=8500$.

Answer:

$8500$