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Chapter 17: Problem 72

12,000\( is borrowed now at 12 percent interest. The first payment is \)\$ 4000\( and is made three years from now. The balance of the debt immediately after the payment is a) \)\$ 4000\( c) \)\$ 12,000\( b) \)\$ 8000\( d) \)\$ 12,860$

Short Answer

Expert verified
Answer: d) 12,860

Step by step solution

01

1. Calculate the future value of the debt after three years

Since the interest rate is 12%, we can calculate the future value of the debt after three years using the compound interest formula: \(FV = P(1 + r)^n\), where \(FV\) is the future value, \(P\) is the principal amount, \(r\) is the interest rate, and \(n\) is the number of years. In this case, \(P = 12000\), \(r = 0.12\), and \(n = 3\). Plugging in the values, we get: \(FV = 12000(1 + 0.12)^3 = 12000(1.12)^3 = 12000(1.404928) \approx 16859.14\).
02

2. Calculate the balance of the loan after the payment

Now, we are given that the first payment made is $4,000. To calculate the balance of the loan immediately after the payment, we need to subtract this payment from the future value of the debt after 3 years: \( Balance = FV - Payment = 16859.14 - 4000 = 12859.14 \approx 12859\). The balance of the debt immediately after the payment is closest to option d) \(12,860\).

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