Spencer takes out a home improvement loan for 30,000 at an interest rate of 5.5%. How much does he owe, and what is his monthly payment if he chooses the 7-year loan payment plan?

11550

Step-by-step explanation:

Formula for calculating simple interest is : Simple Interest=P x R x T/100

Step 1: Identify P, R, T

P: Principal amount-basic amount of the loan (30,000)

R: The interest rate of the loan (5.5%)

T: Time of payment of loan-in years (7 years)

Step 2: Substitute the values

Simple Interest = P x R x T/100

Simple Interest = 30,000 x 5.5 x7

100

Simple Interest = 1155000

100

Simple Interest = 11550

Let's answer the first part of the question: "How much does he owe?"

Step 1: We have calculated simple interest which is 11550.

Step 2: The principal amount has to be paid with the simple interest.

Step 3: Formula - Total money owed = Principal amount + Simple Interest

Total money owed = 30,000 + 11550=41550

Now let's answer the second part of the question: "What is the monthly payment if he chooses the 7-year loan payment plan?"

Step 1: Calculate how many months are there in 7 years. Each year has 12 months therefore 7 years have (7 x 12) 84 months.

Step 2: Divide the total amount that has to be paid by the number of months it has to be paid in.

Monthly payment = Total money owed / total number of months

Monthly payment = 41550 / 84

Monthly payment = 494.64

Use the simple interest formula: A = P (1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

Solving our equation:

A = 30000 (1 + (0.055 * 7)) = 41550

A = $41,550.00

The total amount accrued, principal plus interest, from simple interest on a principal of $30,000.00 at a rate of 5.5% per year for 7 years is $41,550.00.