Question

Jessica’s bank is offering her a loan with a stated rate of 4. 90% interest. If the interest is compounded every two months, what will Jessica really pay for interest? a. 4. 90% b. 5. 00% c. 5. 01% d. 4. 96%.

Answer 1

The correct effective rate of interest for the loan having a compound interest of 4.90% with 6 compounding throughout the year will be 5.01%. So, the correct option is C.

Effective compound interest is calculated by deriving the values in the formula of annuity over the loan amount, which will be payable at the end of the year.

Calculation of effective rate of interest

• Effective rate of interest is the actual rate of interest paid by Jessica when she thinks the interest paid by her is for the year without taking into consideration the compounding of such loan.

• As no information regarding the principal and no. of years is given, it has been assumed that the loan amount is $100 and the loan is taken for the period of one year.

• The formula for calculation of effective rate of interest is as below,

• $\rm Effective\ ROI= (1+ \dfrac{1}{n})^n-1$

• Putting the values in the formula, we get

• $\rm Effective\ ROI= (1+ \dfrac{0.049}{6})^6-1\\\\\\\rm Effective\ ROI= (1+0.0082)^6-1\\\\\\\rm Effective\ ROI= 6.02-1$

• Finally,

• $\rm Effective\ ROI= 5.02$

• So the effective rate of interest is calculated as 5.01%

Hence, the correct option is C that the effective rate of interest is 5.01% on the interest rate of 4.90% compounded 6 times during the year.

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