Question

mr. x borrows 1,00,000 at 8% compounded annually. equal annual payments are to be made for 6 years. however, at the time of the fourth payment, the individual elects to pay off the loan. how much should be paid?

Answer 1

To find out how much should be paid at the time of the fourth payment, we need to calculate the balance remaining on the loan after the third payment. The remaining balance on the loan after the third payment is $32,462.50. Therefore, the individual should pay off this amount at the time of the fourth payment.

Step-by-step explanation:

To find out how much should be paid at the time of the fourth payment, we need to calculate the balance remaining on the loan after the third payment.

We can use the formula for the future value of an ordinary annuity to calculate the remaining balance. The formula is:

FV = P * ( (1 + r)^n - 1 ) / r

Where:

• FV is the future value or remaining balance on the loan
• P is the payment made each year
• r is the interest rate per period (in this case, the annual interest rate divided by the number of compounding periods per year)
• n is the number of periods (in this case, the number of years)
• By plugging in the given values (P = 1,00,000/6, r = 0.08/1 = 0.08, n = 3), we get:

FV = 1,00,000 * ( (1 + 0.08)^3 - 1 ) / 0.08

FV = 1,00,000 * (1.08^3 - 1) / 0.08

FV = 1,00,000 * (1.2597 - 1) / 0.08

FV = 1,00,000 * (0.2597) / 0.08

FV = 32,462.50

So, the remaining balance on the loan after the third payment is $32,462.50. Therefore, the individual should pay off this amount at the time of the fourth payment.