Questions: To help pay for college, David borrowed money from his credit union. He took out a personal, amortized loan for 58,500, at an interest rate of 5.25%, with monthly payments for a term of 10 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 David's monthly payment. (b) If David pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If David pays the monthly payment each month for the full term, find the total amount of interest he will pay.

To help pay for college, David borrowed money from his credit union. He took out a personal, amortized loan for 58,500, at an interest rate of 5.25%, with monthly payments for a term of 10 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 David's monthly payment. (b) If David pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If David pays the monthly payment each month for the full term, find the total amount of interest he will pay.

Transcript text: To help pay for college, David borrowed money from his credit union. He took out a personal, amortized loan for $\$ 58,500$, at an interest rate of $5.25 \%$, with monthly payments for a term of 10 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 David's monthly payment. $\$ \square$ (b) If David pays the monthly payment each month for the full term, find his total amount to repay the loan. $\$ \square$ (c) If David 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

To calculate the monthly payment $M$, we use the formula: \[ M = P \frac{r(1+r)^n}{(1+r)^n-1} \] Substituting $P = 58500$, $r = 0.00438$, and $n = 120$, we get: \[ M = 58500 \frac{0.00438(1+0.00438)^120}{(1+0.00438)^120-1} = 627.66 \]

Step 2: Total Payment Calculation

The total payment $T$ made over the term of the loan is calculated as: \[ T = M \times n \] Substituting $M = 627.66$ and $n = 120$, we get: \[ T = 627.66 \times 120 = 75318.77 \]

Step 3: Total Interest Paid Calculation

The total interest $I$ paid over the term of the loan is calculated as: \[ I = T - P \] Substituting $T = 75318.77$ and $P = 58500$, we get: \[ I = 75318.77 - 58500 = 16818.77 \]