Question

Date of loan: 1/1/2005

Terms of loan repayment: 20 annual payments beginning 12/31/2005

The payment is X in the first 10 years, and 50% of X in the second 10 years

Interest rate: 5%, effective annually

Compute the ratio Y of the principal repaid in the 10th payment to the principal repaid in the 11th payment.

Answer 1

Let the value of X=100

Principal paid in the 20th Installment = (X/2)/1.05 =50/1.05 = 47.62

Principal paid in 19th Installment = {[(X/2)+47.62]/1.05-47.61} = {92.97- 47.61} = 45.35

Principal paid in 18th last Installment = {[(X/2)+92.97]/1.05-92.97} = {136.16- 92.97} = 43.19

Putting the Formula in Excel:

Ratio of (Principal Amount paid in 10th installment/ Principal Amount paid in 11th installment) = 2.503709