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Math  /  Algebra

QuestionTo help pay for art school; Kaitlin borrowed money from an online lending company. She took out a personal, amortized loan for $50,000\$ 50,000, at an interest rate of 5.15%5.15 \%, with monthly payments for a term of 15 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 Kaitlin's monthly payment. \(b)IfKaitlinpaysthemonthlypaymenteachmonthforthefullterm,findhertotalamounttorepaytheloan.$ (b) If Kaitlin pays the monthly payment each month for the full term, find her total amount to repay the loan. \$ \square(c)IfKaitlinpaysthemonthlypaymenteachmonthforthefullterm,findthetotalamountofinterestshewillpay.$ (c) If Kaitlin pays the monthly payment each month for the full term, find the total amount of interest she will pay. \$ \square$

Studdy Solution

STEP 1

1. Kaitlin borrowed $50,000.
2. The interest rate is 5.15% per annum.
3. The loan term is 15 years.
4. Payments are made monthly.
5. We will use the standard amortization formula for monthly payments.
6. We will calculate the total repayment and total interest paid over the term.

STEP 2

1. Calculate the monthly payment using the amortization formula.
2. Calculate the total amount to repay the loan.
3. Calculate the total amount of interest paid over the term.

STEP 3

Calculate the monthly payment using the amortization formula.
The formula for the monthly payment M M is given by:
M=Pr(1+r)n(1+r)n−1 M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
Where: - P=50000 P = 50000 is the principal loan amount. - r=5.15100×12=0.051512 r = \frac{5.15}{100 \times 12} = \frac{0.0515}{12} is the monthly interest rate. - n=15×12=180 n = 15 \times 12 = 180 is the total number of payments.
Substitute the values into the formula:
M=500000.051512(1+0.051512)180(1+0.051512)180−1 M = 50000 \frac{\frac{0.0515}{12}(1 + \frac{0.0515}{12})^{180}}{(1 + \frac{0.0515}{12})^{180} - 1}
Calculate M M .

STEP 4

Calculate the total amount to repay the loan.
The total repayment amount T T is given by:
T=M×n T = M \times n
Substitute the values:
T=M×180 T = M \times 180
Calculate T T .

STEP 5

Calculate the total amount of interest paid over the term.
The total interest I I is given by:
I=T−P I = T - P
Substitute the values:
I=T−50000 I = T - 50000
Calculate I I .

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