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When calculating the effective rate of a loan, which statement or statements must be true if n is equal to 1?

i. the nominal rate equals the effective rate.
ii. the length of the loan is exactly one year.
iii. the interest is compounded annually.
a. i and iii
b. ii and iii
c. i only
d. iii only

User BB Design
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1 Answer

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Final answer:

To calculate the effective rate of a loan when n is equal to 1, both statement ii and iii must be true. Statement ii states that the length of the loan is exactly one year, and statement iii states that the interest is compounded annually.

Step-by-step explanation:

To calculate the effective rate of a loan when n is equal to 1, both statement ii and iii must be true. Statement ii states that the length of the loan is exactly one year, which means that the loan duration is one year.

Statement iii states that the interest is compounded annually, which means that the interest is calculated and added to the loan balance once a year. When calculating the effective rate of a loan and n is equal to 1, it must be true that the nominal rate equals the effective rate as there is no effect of compounding on the interest if it is compounded annually only once.

Therefore, statement i is true. However, it is not necessary for the length of the loan to be exactly one year (statement ii) or for the interest to be compounded annually (statement iii) for the nominal rate to equal the effective rate when n is 1.

Therefore, the correct answer is option b. ii and iii.

User Dan Nestor
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