an amount of $41,000 is borrowed for 7 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of that year, how much must be paid back?

Question

Mathematics

Moreno

24 February, 17:04

an amount of $41,000 is borrowed for 7 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of that year, how much must be paid back?

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Answers (1)

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Yael Mcintosh · Answer 1

We must pay back US$ 64,767.70 for the loan after 7 years.

Step-by-step explanation:

1. Let's review the data given to us for answering the question:

Loan amount = US$ 41,000

Duration of the loan = 7 years

Interest rate = 6.75% compounded annually

2. Let's find the future value of this loan after 7 years, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Loan = US$ 41,000

number of periods (n) = 7 (7 years compounded annually)

rate (r) = 6.75% = 0.0675

Replacing with the real values, we have:

FV = 41,000 * (1 + 0.0675) ⁷

FV = 41,000 * (1.0675) ⁷

FV = 41,000 * 1.5797

FV = US$ 64,767.70

We must pay back US$ 64,767.70 for the loan after 7 years.