Given the APR (r %), the principal (P) and the term for the loan (n), calculation of monthly payment (X) is

computed as follows

𝑋

𝑃=

𝑟(1 + 𝑟)𝑛

(1 + 𝑟)𝑛 − 1

Let us first calculate the payment per month using the formula.

𝑟 = 15% (0.15); 𝑛 = 10 × 12 = 120 𝑚𝑜𝑛𝑡ℎ𝑠; 𝑃 = $8,500

𝑋 = 𝑃(1.15)120

1.15120 − 1= $137.13

Here is the schedule for the first 12 months showing principal, interest and balance from the excel

spreadsheet based on the monthly payment calculation from the formula.

Period Payment Principal Part Interest Part Balance

1 $137.13 $30.88 $106.25 $8,469.12

2 $137.13 $31.27 $105.86 $8,437.84

3 $137.13 $31.66 $105.47 $8,406.18

4 $137.13 $32.06 $105.08 $8,374.13

5 $137.13 $32.46 $104.68 $8,341.67

6 $137.13 $32.86 $104.27 $8,308.80

7 $137.13 $33.27 $103.86 $8,275.53

8 $137.13 $33.69 $103.44 $8,241.84

9 $137.13 $34.11 $103.02 $8,207.73

10 $137.13 $34.54 $102.60 $8,173.19

11 $137.13 $34.97 $102.16 $8,138.22

12 $137.13 $35.41 $101.73 $8,102.81

𝐴𝑚𝑜𝑢𝑛𝑡 𝑝𝑎𝑖𝑑 = 𝑋 × 𝑛 = 137.13 × 120 = $16,456.17

𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝐴 − 𝑃 = $7,956.17

Part a:

It is clear that the payment of $106.25 is obviously less than what is required to pay off the principal as well.

Calculate the interest only for the first based on simple rate.

𝐼 = 8,500(. 15)

12= $106.25

We see that the payment required matches this. Hence the calculation is not based on amortization but

interest only.

Part c:

Interest paid as requested by the company:

𝐼 = (𝑝)(𝑛)(12) = 106.25 × 120 = $12,750

Remember the money borrowed is not paid off. So technically you owe the company that $8,500 at the end

of 10 years. This is the disadvantage in interest only payments. The monthly payments are low but, you end

up paying more overall, if you choose to pay off the $8,500 at the end of the term. ($21,250)

The interest that you pay through amortization is shown above as $ 7,956.17

You would save by paying a little more every month as it is applied towards principal and so the interest paid

on a monthly basis will reduce, thus accruing more towards principal.

You would save about $21,250 − $16456.17 = $4,973.83 over the period of the loan.