Question

The following data relates to the next 6 questions: Suppose you owe $10,000 on your credit card. The APR for the card is 18%. Assume you do not charge anymore amounts to this card.

13. Suppose you wish to payoff your balance in two years, what is the monthly payment you need to make? a. $251.43 b. $445.47 c. $499.24 d. $651.85 e. $832.95

14. If you make the payments calculated in the previous question, how much do you owe on your card after 1 year (immediately after 12th payment)? a. $3,251.43 b. $5,445.47 c. $7,499.24 d. $8,651.85 e. $9,832.95

Answer 1

(13)-Monthly Loan Payment

Loan Amount (P) = $10,000

Monthly Interest Rate (n) = 1.50% per month [18% / 12 Months]

Number of months (n) = 24 Months [2 Years x 12 Months]

Monthly Loan Payment = [P x {r (1+r)n} ] / [( 1+r)n – 1]

= [$10,000 x {0.015 x (1 + 0.015)²⁴}] / [(1 + 0.015)²⁴ – 1]

= [$10,000 x {0.015 x 1.429502}] / [1.429502 – 1]

= [$10,000 x 0.0214425] / 0.429502

= $499.24 per month

“Monthly Loan Payment = (c). $499.24”

(14)-Balance remaining immediately after 12th payment

Remaining Balance of a Mortgage Loan is calculated by using the following formula

Remaining Balance = [Amount Borrowed x (1 + r) ⁿ] – [Monthly Payment x {{(1 + r)ⁿ -1}/ r]

Loan Amount (P) = $10,000

Monthly Interest Rate (n) = 1.50% per month [18% / 12 Months]

Number of months (n) = 12 Months [1 Years x 12 Months]

Remaining Balance = [Amount Borrowed x (1 + r) ⁿ] – [Monthly Payment x {{(1 + r)ⁿ -1}/ r]

= [$10,000 x (1 + 0.015)¹²] – [$499.24 x {{(1 + 0.015)¹² -1}/ 0.015]

= [$10,000 x 1.1956182] – [$499.24 x {( 1.1956182 – 1) / 0.015}]

= [$10,000 x 1.1956182] – [$499.24 x (0.195618 / 0.015)]

= $11,956.18 – $6,510.71

= $5,445.47

“Hence, the balance owe on your card after 1 year (immediately after 12th payment) = (b). $5,445.47”