Question

If a musician uses his credit card to pay for a new violin that costs $2,900 and does not pay on it until the second month, what will the 3.35% monthly interest charge be at the end of the first month? Show your work or explain how you got your answer.
Calculate the total payback for a $3,500 loan at 8% annual interest with monthly payments for two years. Show all of your steps.

Use the formula, M = Pm(1 + m)^na/(1 + m)^na - 1, as needed.

Answer 1

Solution:

1.  Cost of a new Violin that is bought by the musician = $ 2900

Monthly interest charge = 3.35 %

If you will find the compound interest or simple interest for a month, they both will be same for a month.

Simple interest =

$\frac{Principal \times Rate \times Time}{100}$

 $=\frac{2900 \times 3.35 \times 1}{ 100}\\\\ =29 \times 3.35\\\\ =97.15$

Interest paid at the end of first month = $ 97.15

2. Loan Amount = $ 3,500

Annual interest = 8 %

Time period = 2 years= 24 months

As , we have to find the  total payback  for two years, at 8% annual interest with monthly payments .we will use the formula of Amount in terms of compound interest here.

Formula for Amount

Amount= $Principal (1 +\frac{Rate}{100})^{time}]$

          $=3500 \times [(1+\frac{8}{1200})^{24}]\\\\ = 3500 \times [(1.0066)^{24}]\\\\= 3500 \times 1.1710 \\\\ =4098.58$

Total payback after 2 years = $ 4098.58