SOLUTION: BofA offer two programs for a car loan, 1st program offer is based on simple interest of 6.8% for four years. The 2nd program is based on a compound monthly with interest rate of 5

Question 849282: BofA offer two programs for a car loan, 1st program offer is based on simple interest of 6.8% for four years. The 2nd program is based on a compound monthly with interest rate of 5.5% for four years. Joan is considering to borrow $12,500 to buy a car and ask your opinion for the loan. Which loan would you suggest to her and why. How much interest she will pay on both loans after 32 months?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Simple Interest Loan:
I = P * R * T
I = interest
P = principal
R = Interest Rate per Time Period
T = Number of Time Periods

In your problem:

P = 12,500
R = .068 per year.
T = 4 years
I = Interest

Replace P with 12,500 and R with .068 and T with 4 and the simple interest formula becomes:

I = 12,500 * .068 * 4 = $3,400.

Compound Interest Loan:

F = P * (1+R)^T
I = F - P

Combine these formulas together and you get:

I = P * (1+R)^T - P

Simplify this formula further using the distributive law and you get:

I = P * ((1+R)^T - 1)

You can use the formula in either form to get your answer.

The forms are:

F = P * (1+R)^T
I = F - P

I = P * (1+R)^T - P

I = P * ((1+R)^T - 1)

I used the first form which calculates the future value of the loan first and then calculates the interest by subtracting the principal.

F = Future Value of the loan which is the amount you have to pay back at maturity.
P = Principal or what is also known as the Present Value of the loan.
R = Interest Rate per Time Period
T = Number of Time Periods.
I = Interest

In your problem:

P = 12,500
R = .055 per year divided by 12 months = .00458333 per month.
T = 4 years * 12 compounding periods per year = 48 months.

Replace P with 12,500 and R with .00458333 and T with 48 and the compound interest formula becomes:

F = 12,500 * (1.0094583)^48 = $15,568.

Replace F with 15,568 and the I = F - P formula becomes:

I = 15,568 - 12,500 = $3,068.

She should take the second loan because she will pay over $300.00 less in interest over the 4 year period.

After 32 months, the interest on the simple interest loan will be equal to:

I = P * R * T = 12,500 * l068 * (32/12) = $2,266.67

Since T is in years, you need to divide 32 by 12 to get the equivalent number of years.

After 32 months, the interest on the compound interest loan will be equal to:

F = P * (1 + R) ^ T = 12,500 * (1.004583333) ^ 32 = 14,469.75 - 12,500 = $1,969.75

With simple interest, you can calculate the interest directly.
With compound interest, you have to calculate the future value of the loan and then subtract the principal from that to get the interest.

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