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 =
[tex]\frac{Principal \times Rate \times Time}{100}[/tex]
[tex]=\frac{2900 \times 3.35 \times 1}{ 100}\\\\ =29 \times 3.35\\\\ =97.15[/tex]
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= [tex]Principal (1 +\frac{Rate}{100})^{time}][/tex]
[tex]=3500 \times [(1+\frac{8}{1200})^{24}]\\\\ = 3500 \times [(1.0066)^{24}]\\\\= 3500 \times 1.1710 \\\\ =4098.58[/tex]
Total payback after 2 years = $ 4098.58
The values are $97.15 and $170.1.
Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Given
Rate (r) = 3.35%
Principal (P) = $2900
Calculate the total payback.
We know the formula of compound interest,
[tex]\rm Amount = Principal ( \dfrac{Rate}{100})^{Time}[/tex]
Then put the values,
[tex]\rm Amount = 2900( \dfrac{2.7}{100})^{1}\\\\\rm Amount = 2900(0.027)\\\\Amount = 97.15\\[/tex]
Then for the annual
P = $3500
R = 8%
T = 2
Then
[tex]\rm Amount = 3500(1+ \dfrac{8}{100})^{2}\\\\\rm Amount = 3500(1.08)^2\\\\Amount = 4082.4\\[/tex]
Then for months, it will be
4082.4 / 24 = 170.1
Thus the values are $97.15 and $170.1.
More about the compound interest link is given below.
https://brainly.com/question/25857212
