Question

Richard has a credit card that allows him to defer credit card payments for 1 year if he becomes unemployed. The interest on the card debt continues to accrue, but there are no late payment penalties. Suppose Richard has $1,588.57 in credit card debt, and the annual interest rate is 24.5% compounded monthly. How much will Richard owe (in dollars) after 1 year if he takes advantage of this option? Assume he makes no other purchases with the card. (Enter a number. Round your answer to the nearest cent.)

Answer 1

Answer: Richard will owe $2024 after 1 year if he takes advantage of this option.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1588.57

r = 24.5% = 24.5/100 = 0.245

n = 12 because it was compounded 12 times in a year.

t = 1 year

Therefore,.

A = 1588.57(1+0.245/12)^1 × 12

A = 1588.57(1+0.245/12)^12

A = 1588.57(1+0.0204)^12

A = 1588.57(1.0204)^12

A = $2024.2