Question

A loan made today is to be repaid by payments of $888.49 at the end of each month for the next 12 months (with the first payment to be made one month from now). if the interest rate is 12% per annum compounded monthly, the amount borrowed is (to the nearest dollar)

a. $9,901
b. $11,268
c. $10,000
d. $10,100

Answer 1

To find the amount borrowed, you can use the present value formula PV = R × [1 - (1 + i)^(-n)] / i, where PV is the present value (amount borrowed), R is the monthly payment, i is the monthly interest rate, and n is the number of payments. Plugging in the given values, the amount borrowed is approximately $10,100.

Step-by-step explanation:

To find the amount borrowed, we can use the present value formula:

PV = R × [1 - (1 + i)^(-n)] / i

Where:

• PV is the present value (amount borrowed)
• R is the monthly payment ($888.49)
• i is the monthly interest rate (12% divided by 12)
• n is the number of payments (12)

Plugging in the values, we have:

PV = $888.49 × [1 - (1 + 0.01)^(-12)] / 0.01

Solving this equation, we find that the amount borrowed is approximately $10,100 (option d).