Chapter 7.7, Problem 23PPS

To determine

To calculate: The number of months for the loan.

Answer to Problem 23PPS

The number of months is 31.5 months.

Explanation of Solution

Given information: The amount of car loan is $8000. Rate of simple interest is 8%. The amount of interest is $1680.

Formula used: The simple interest formula is $S.I=P\times r\times t$

Where, S.I = simple interest amount, P = principal amount, r =annual rate of interest, t = the length of time the money is invested.

Calculation:

In the problem given,

S.I = $1680, P = $8000, r= 8%= $\frac{8}{100}$ = $0.08$

1 year = 12 months

Monthly rate of interest = $\frac{r}{12}$ = $\frac{0.08}{12}$

  $S.I=P\times r\times t$

  $\Rightarrow 1680=8000\times \frac{0.08}{12}\times t$

  $\Rightarrow 1680=\frac{8000\times 0.08}{12}\times t$

  $\Rightarrow 1680=\frac{640}{12}\times t$

  $\Rightarrow 1680\times 12=640\times t$

  $\Rightarrow 20160=640\times t$

  $\Rightarrow t=\frac{20160}{640}$

  $\Rightarrow t=31.5$

The number of months of the loan was 31.5 months.