Question

assuming that five years later, interest rates drop to 3.2% and shanna decides to refinance the mortgage. how much would she have paid in interest and how much of the original loan have you paid over the five years?

Answer 1

To find the interest from a $5,000 loan at a 6% simple interest rate over three years, apply the formula I = PRT, resulting in a total interest of $900. For a loan of $10,000 where $500 in interest is received after five years, the interest rate is determined to be 1% when using the rearranged formula R = I / (P x T).

Step-by-step explanation:

When calculating the total amount of interest from a $5,000 loan with a simple interest rate of 6% over three years, the formula for simple interest, which is I = PRT (Interest = Principal x Rate x Time), can be used. Here, the principal (P) is $5,000, the rate (R) is 6% or 0.06 when converted to a decimal, and the time (T) is 3 years. Plugging these values into the formula gives us:

I = $5,000 x 0.06 x 3 = $900

The total amount of simple interest paid over the three years will thus be $900.

Now, for the second calculation, if you receive $500 in simple interest on a loan of $10,000 for five years, we rearrange the simple interest formula to solve for the rate (R): R = I / (P x T). Here, the interest (I) received is $500, the principal (P) is $10,000, and the time (T) is 5 years. The calculation will look like this:

R = $500 / ($10,000 x 5) = 0.01

Therefore, the interest rate charged on the loan is 1%.

Answer 2

Shanna would have paid a lower amount in interest after refinancing due to the reduced interest rate of 3.2%.

Step-by-step explanation:

Shanna's decision to refinance her mortgage at a lower interest rate of 3.2% after five years has financial implications. Firstly, a lower interest rate means that the cost of borrowing decreases. This results in Shanna paying less in interest compared to the original mortgage. The interest paid is influenced by the interest rate, loan amount, and the time the loan is outstanding.

To calculate the new interest paid, one would typically use the formula for compound interest. The reduced interest rate would lead to a lower interest accrual over the remaining term of the loan. This lower interest expense contributes to potential overall savings for Shanna.

The amount of the original loan that Shanna has paid over the five years is determined by the loan amortization schedule. As Shanna makes monthly payments, a portion goes towards interest, and the rest reduces the principal amount. With the reduced interest rate during refinancing, a larger portion of each payment contributes to reducing the principal, accelerating the equity build-up.

In conclusion, Shanna would pay less in interest after refinancing at 3.2%, and a higher percentage of her original loan would be paid off due to the favorable interest rate.