Questions: Consumer Mathematics Finding the monthly payment, total payment, and interest for a loan To help open up a restaurant, Ryan borrowed money from an online lending company. He took out a personal, amortized loan for 44,500, at an interest rate of 6.25%, with monthly payments for a term of 7 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Ryan's monthly payment. (b) If Ryan pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If Ryan pays the monthly payment each month for the full term, find the total amount of interest he will pay.

Consumer Mathematics
Finding the monthly payment, total payment, and interest for a loan

To help open up a restaurant, Ryan borrowed money from an online lending company.

He took out a personal, amortized loan for 44,500, at an interest rate of 6.25%, with monthly payments for a term of 7 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Ryan's monthly payment.

(b) If Ryan pays the monthly payment each month for the full term, find his total amount to repay the loan.

(c) If Ryan pays the monthly payment each month for the full term, find the total amount of interest he will pay.

Transcript text: Consumer Mathematics Finding the monthly payment, total payment, and interest for a loan To help open up a restaurant, Ryan borrowed money from an online lending company. He took out a personal, amortized loan for $\$ 44,500$, at an interest rate of $6.25 \%$, with monthly payments for a term of 7 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Ryan's monthly payment. $\$ \square$ (b) If Ryan pays the monthly payment each month for the full term, find his total amount to repay the loan. $\$ \square$ (c) If Ryan pays the monthly payment each month for the full term, find the total amount of interest he will pay. $\$$

Solution

Solution Steps

Step 1: Monthly Payment Calculation

The monthly payment can be calculated using the formula: $$M = P \frac{r/12}{1 - (1 + r/12)^{-12n}}$$ Substituting the given values: $$M = 44500 \frac{0.0052}{1 - (1 + 0.0052)^{-12*7}}$$ This gives us a monthly payment of: $$M = 655.43$$

Step 2: Total Payment Calculation

The total payment is calculated as the monthly payment times the total number of payments: $$Total\ Payment = M \times 12n$$ Substituting the values: $$Total\ Payment = 655.43 \times 12 \times 7$$ This gives us a total payment of: $$Total\ Payment = 55055.88$$

Step 3: Total Interest Calculation

The total interest paid over the term of the loan is the total payment minus the principal amount: $$Total\ Interest = (M \times 12n) - P$$ Substituting the values: $$Total\ Interest = (655.43 \times 12 \times 7) - 44500$$ This gives us a total interest of: $$Total\ Interest = 10555.88$$