Respuesta :

semsee45

Answer:

$6,208.93

Step-by-step explanation:

Find the total interest for a 15-month loan of $98,359.25 if the simple interest rate is 5.05%, we can use the simple interest formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Simple Interest Formula}}\\\\I = Prt\\\\\textsf{where:}\\\\ \phantom{ww}\bullet\;\textsf{$I$ is the total interest.}\\ \phantom{ww}\bullet\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\\ \end{array}}[/tex]

In this case:

  • P = $98,359.25
  • r = 5.05% = 0.0505
  • t = 15/12 years (since there are 12 months in a year) = 1.25 years

Substitute the values into the formula and solve for I:

[tex]I=98359.25\cdot 0.0505 \cdot 1.25[/tex]

[tex]I=4967.142125 \cdot 1.25[/tex]

[tex]I=6208.92765625[/tex]

[tex]I=\$6208.93[/tex]

Therefore, the total interest is $6,208.93 (rounded to the nearest cent).

msm555

Answer:

$6,208.93

Step-by-step explanation:

The formula for calculating simple interest is given by:

[tex] \textsf{Simple Interest} = \dfrac{P \times T \times R}{100} [/tex]

where:

  • [tex] P [/tex] is the principal amount (initial loan amount),
  • [tex] T [/tex] is the time (in years), and
  • [tex] R [/tex] is the interest rate per annum.

In this case:

  • [tex] P = \$98,359.25 [/tex],
  • [tex] T = \dfrac{15}{12} [/tex] years (15 months converted to years),
  • [tex] R = 5.05\% [/tex].

Now substitute these values into the formula:

[tex] \textsf{Simple Interest} = \dfrac{98,359.25 \times \dfrac{15}{12} \times 5.05}{100} [/tex]

Calculate the result:

[tex] \textsf{Simple Interest} \approx \dfrac{98,359.25 \times \dfrac{15}{12} \times 5.05}{100} [/tex]

[tex] \textsf{Simple Interest} \approx \dfrac{98,359.25 \times 1.25 \times 5.05}{100} [/tex]

[tex] \textsf{Simple Interest} \approx \dfrac{122949.0625 \times 5.05}{100} [/tex]

[tex] \textsf{Simple Interest} \approx \dfrac{620892.7656}{100} [/tex]

[tex] \textsf{Simple Interest} \approx 6208.927656 [/tex]

[tex] \textsf{Simple Interest} \approx 6208.93 \textsf{ (in 2 d.p.)} [/tex]

So, the simple interest for a 15month loan of $98,359.25 at a rate of 5.05% is approximately $6,208.93.