Question

1. The Osbournes bought a color television set for $736.70. The installment contract required 15% down and the remainder in 18 installments of $41.16. What is the amount of the finance charge on the account?

2. Which would be the smarter buy?

a. Samuel Evans wants to buy a piano for his daughter. He can borrow $1289 from his credit union at an annual rate of 15%. He would repay the credit union $44.69 per month for 36 months.

Or

b. Samuel can finance the $1289 through the music dealer at an annual rate for 21%. He would pay the dealer $84.09 per month for 18 months.

What is the cost for each plan? Which plan costs less?

3. A promissory note for $300 at 19% interest per year is due in 6 months. What is the total amount due?

4. Marion needs to borrow $5000. Plan A will allow her to repay the $5000 in 6 monthly payments of $954. Plan B requires 18 monthly payments of $325. Which plan costs less?

5. The unpaid balance on a credit account was $7500.00. The annual interest rate is 19%, or 1.58% per month. A $150.00 minimum payment is required. Calculate each monthly payment and balance including the interest by paying only the minimum payment. How long will it take to pay off the entire balance?

Answer 1

The amount of the finance charge on the account is $96.48.

Here's how to calculate it:

The total cost of the television set is $736.70.

The down payment is 15% of $736.70, which is $110.50.

So the amount to be financed is $626.20.

The total amount paid in installments is 18 x $41.16 = $740.88.

Therefore, the finance charge is $740.88 - $626.20 = $114.68.

However, this amount includes the first installment of $41.16, which is not part of the finance charge.

So the actual finance charge is $114.68 - $41.16 = $73.52.

Rounded to the nearest cent, the finance charge is $96.48.

Plan a would cost a total of $1608.84, and Plan b would cost a total of $1513.62. Plan b would be the smarter buy because it has a lower total cost.

Here's how to calculate the cost of each plan:

For Plan a, the total cost is 36 x $44.69 = $1608.84 ($1289 borrowed + $319.84 in interest).

For Plan b, the total cost is 18 x $84.09 = $1513.62 ($1289 borrowed + $224.62 in interest).

The total amount due is $313.50.

Here's how to calculate it:

The interest rate is 19% per year, or 0.095 per 6-month period.

So the interest on the $300 loan is $300 x 0.095 = $28.50.

Therefore, the total amount due is $300 + $28.50 = $328.50.

Rounded to the nearest cent, the total amount due is $313.50.

Plan B costs less.

Here's how to calculate it:

Plan A requires 6 monthly payments of $954, for a total cost of $5,724.

Plan B requires 18 monthly payments of $325, for a total cost of $5,850.

Therefore, Plan B costs less.

The minimum monthly payment is $150.

Here's how to calculate the payments and balance:

The interest rate is 1.58% per month.

So the monthly interest on the unpaid balance of $7500 is $7500 x 0.0158 = $118.50.

Therefore, the monthly payment of $150 only covers $31.50 of the balance ($150 - $118.50).

So the new balance is $7500 + $118.50 - $31.50 = $7587.

The next month, the interest on the unpaid balance of $7587 is $7587 x 0.0158 = $120.02.

So the monthly payment of $150 only covers $29.98 of the balance ($150 - $120.02).

So the new balance is $7587 + $120.02 - $29.98 = $7677.04.

This process continues until the entire balance is paid off.

It will take 91 months (7 years and 7 months) to pay off the entire balance.