Question

A promissory note for ​$800 dated ​jan 15​, 2017requires an interest payment of ​$ 120at maturity. If interest is at ​% 9p.a. compounded ​, determine the due date of the note.

round to the nearest day

Answer 1

The due date of the note is on August 16, 2017.

Given data, principal amount = $800, interest = $120, and interest rate (r) = 9% per annum. We need to calculate the due date of the promissory note.

Step 1: Determine the maturity value of the note. Since the interest is compounded, we need to use the formula: Amount =
`Principal (1 + r/n)^((n*t))`, where n is the number of times interest is compounded in a year, and t is the time in years. After substituting the values, we have:. Therefore,$920/$800 = (1.09)^t1.15 = (1.09)^tt = log₁.₀₉(1.15)t = 0.48 year = 0.48 × 365 days (rounding off to the nearest day)≈ 175 days

Step 2: Determine the due date of the note Jan 15, 2017 + 175 days = Jul 10, 2017Due to the interest payment of $120 at maturity, we need to add another 36 days. Jul 10, 2017 + 36 days = Aug 16, 2017Therefore, the due date of the promissory note is on August 16, 2017.