Question

The nominal rate on Sarah’s loan is 7. 250%. If the interest is compounded monthly, what rate of interest is Sarah actually paying? a. 7. 250% b. 7. 496% c. 7. 510% d. 8. 700%.

Answer 1

In this example, Sarah is actually paying interest, which is compounded monthly at the rate of 7.496%. So, the correct option that matches the above statement is B.

Compound interest can be easily calculated by the way of putting the values given in the formula for compound interest, which is compounded on a monthly basis.

Calculation of Compound Interest

• Compound interest is best defined with the terms as interest given on accrued interest or the accumulated interest in addition to the interest on the principal amount.

• In the example, the amount of loan is not given. Hence, we are assuming that Sarah took a loan of $10000. It is also not provided that the tenure of the loan taken by Sarah, so we are assuming the time period as one year.

• The formula to calculate Compound interest is as given below,

• $\rm Compound\ Interest= Principal\ Amount\ x\ (1+ \dfrac {r}{n})^n^t$

• In the formula above r is denoted as rate of interest, n is the number of times such interest is paid throughout the tenure and t is the time. So putting the assumed values in the formula, we get,

• $\rm {Compound\ Interest} = \ 10000\ x\ (1+ \dfrac {0.0725}{12})^1^2\ x\ 1\\\\\\\\\rm {Compound\ Interest} = \ 10749.58\\\\\\Actual\ Interest\ Earned= 10749.58-10000$

• So the actual interest actually paid will be $749.58 for the period of 1 year from such calculation.

• If we calculate such interest paid, the effective rate of interest paid by Sarah will account to 7.496% (rounded off to three decimal places).

Hence, we can say that Sarah will be actually paying the interest at the rate of 7.496% and that the correct option is B.

To know more about compound interest, click the link below.

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