Question

Colin borrowed some money at 7.16%/a compounded quarterly. Three years later, he paid $5000 toward the principal and the interest. After another two
he paid another $5000. After another five years, he paid the remainder of the principal and the interest, which totalled $5000. How much money
did he originally borrow?

Answer 1

Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.

How do we calculate the original amount using PV formula?

To solve this question, the following present value (PV) formula will be used:

PVn = Pn / (1 + r)^n ........................... (1)

Where:

PVn = Present value of an amount paid in year n

P = Amount paid in year n

r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179

n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4

Using equation (1), we can therefore proceed as follows:

PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18

PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45

PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04

Therefore, we have:

Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67

Learn more about borrowing here: brainly.com/question/4239348.

#SPJ1