Question

a) You took out a one-year loan for $1000 and agreed to pay it in three equal installments, one payment at the end of 1 month, second payment at the end of 2 months, and the last payment at the end of the year. What is the size of each payment? Assume the interest rate is 9%.

b) In part (a), suppose that you made three non-equal payments: the first was $500 at the end of 1 month, the second was $900 at the end of 2 months and the final payment was $X at the end of the year. What is the value of X if the interest rate is 8%? Use the declining balance method.

Answer 1

a. Loan Amount = Payment at month1 / (1 + Interest per month) + Payment at month 2 / (1 + Interest per month * 2) + Payment at month 12 / (1 + Interest per Year)

1000 = X / 1.0075 + X / 1.015 + X / 1.09

1000 = 3.2271375 * X / 1.11465

X = Size of payment = $345.40

b. Loan Amount = Payment at month1 / (1 + Interest per month) + Payment at month 2 / (1 + Interest per month * 2) + Payment at month 12 / (1 + Interest per Year)

1000 = 500 / 1.0067 + 900 / 1.0133 + X / 1.08

1000 = 496.28 + 886.70 + X / 1.09

X = -384.85 * 1.08

X = -$356.34