Question

Matty Kaminsky owns a new Volvo. His June monthly interest is $400. The rate is 8 ½%. Matty's principal balance at the beginning of June is (use 360 days):

Answer 1

Matty Kaminsky's principal balance at the beginning of June, based on a monthly interest of $400 and an annual rate of 8.5%, is approximately $56,497.18, calculated using the simple interest formula and accounting for the conversion to a monthly rate.

Step-by-step explanation:

The student's question involves calculating the principal balance of Matty Kaminsky's loan based on the provided monthly interest and annual interest rate using a 360-day year. To find the principal balance at the beginning of June, we use the formula for simple interest: Interest = Principal × rate × time. Given that the monthly interest is $400 and the rate is 8.5% (0.085) per year, we divide the rate by 12 to get the monthly rate and then rearrange the formula to solve for Principal. We find that Principal = Interest / (monthly rate × time). The time is expressed in years, so for a one-month period, we use 1/12.

Therefore, the principal balance that Matty has at the beginning of June is:

Principal = $400 / (0.085/12 × 1/12)

Principal = $400 / (0.00708…)

Principal = approximately $56,497.18

This illustration demonstrates the use of simple interest formulas to determine principal amounts and how they relate to monthly payments and interest rates.

Answer 2

$56,470.59

Step-by-step explanation:

We need to calculate the principal amount at the beginning of June

Data:

Interest (I) = $400

Rate(r) = 8.5%

Time(t) = 360 days

Solution:

We can calculate the principal amount by rearranging the Interest calculation formula

Formula: I = Prt

Note; Where P in the formula is the principal amount

Now rearrange the formula in order to find principal

P = I/rt

P = $400/(0.085)x(30/360)

P = $400/(0.085)x(0.08333333333333)

P = $400/(0.00708333333333

P = $56,470.59

Note: we only need to find the principal balance of June so we will consider only 30 days of June out of 360 days.