Asked by Sonia Nelson on Jul 08, 2024

Verified

What is the monthly compounded nominal rate that is equivalent to 7.8% compounded semi-annually?

A) 6.40%

B) 7.68%

C) 8.12%

D) 3.90%

E) 5.88%

A) 6.40%

B) 7.68%

C) 8.12%

D) 3.90%

E) 5.88%

Monthly Compounded

Interest calculation method where interest is added to the principal balance every month, increasing the amount on which future interest is calculated.

Nominal Rate

The stated interest rate of an investment or loan, not including the effect of compound interest or inflation adjustments.

- Adapt nominal interest rates across varying compounding intervals.

Verified Answer

KC

Kimberly Camacho

2 days ago

Final Answer :

B

Explanation :

To find the equivalent monthly compounded nominal rate from a semi-annual rate, we use the formula for converting interest rates: $(1+2r_{SA} )_{2}=(1+12r_{M} )_{12}$ , where $r_{SA}$ is the semi-annual rate and $r_{M}$ is the monthly rate. Given a 7.8% semi-annual rate, or 0.078, we solve for $r_{M}$ . Rearranging and solving gives an equivalent monthly rate of approximately 7.68%.

## Learning Objectives

- Adapt nominal interest rates across varying compounding intervals.

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