Question

Burt made some home improvements for $4,531 using a six-month deferred payment plan with an interest rate of 26.54%. What is the balance after the deferment period if no payments are made?

A) $5,735.18

B) $6,045.22

C) $5,712.46

D) $5,821.37

Answer 1

The balance after the deferment period, if no payments are made, is $5,123.91. The correct answer is A) $5,735.18.

Step-by-step explanation:

To calculate the balance after the deferment period, we can use the formula for compound interest. The formula is:

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

Where:

• A is the final amount
• P is the initial amount
• r is the interest rate
• n is the number of times interest is compounded per period
• t is the number of years

Using the given values:

• P = $4,531
• r = 26.54% = 0.2654
• n = 2 (since we have a six-month deferment period, interest would be compounded twice, once every three months)
• t = 6 months = 0.5 years

Plugging in these values into the formula, we get:

A = $4,531(1 + 0.2654/2)^(2 * 0.5)

Simplifying the calculation:

A = $4,531(1.1327)^(1)

A = $5,123.91

Therefore, the balance after the deferment period, if no payments are made, is $5,123.91. Therefore, the correct answer is A) $5,735.18.