Question

Help with this please.

Answer 1

• payment: $179.95
• total repaid: $43,188
• interest repaid: $23,188
• to principal: 46.3%
• to interest: 53.7%

Explanation:

You want the monthly payment, total paid, interest paid, and the fractions of the total paid that are principal and interest for a 12-year loan of $20,000 at 9%.

a. Monthly payment

The loan payment formula applies. P = 20000, APR = 0.09, n = 12, T = 12.

`\text{pmt}=\frac{P\left(\frac{\text{APR}}{n}\right)}{\left[1-\left(1+\frac{\text{APR}}{n}\right)^(-nT)\right]}\\\\\\\text{pmt}=\frac{20000\left(\frac{\text{0.09}}{12}\right)}{\left[1-\left(1+\frac{\text{0.09}}{12}\right)^(-12\cdot20)\right]}=(20000(0.0075))/(1-1.0075^(-240))\approx 179.95`

The monthly payment is $179.95.

b. Total paid

The sum of 240 payments of 179.95 is ...

240 · $179.95 = $43,188

The total amount repaid will be $43,188.

c. Interest paid

The amount of interest paid is the difference between the total repaid and the principal amount of the loan:

interest = total - principal

interest = $43,188 -20,000 = $23,188

The amount of interest paid is $23,188.

d. Toward principal

The fraction that goes to the principal is ...

20,000/43,188 × 100% ≈ 46.3%

About 46.3% of the amount repaid goes to principal.

e. Toward interest

The remaining amount goes to interest:

100% -46.3% = 53.7%

About 53.7% of the amount repaid goes to interest.

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