Asked by Sonia Nelson on Jul 08, 2024

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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%

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.
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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+rSA2)2=(1+rM12)12 (1 + \frac{r_{SA}}{2})^2 = (1 + \frac{r_M}{12})^{12} (1+2rSA)2=(1+12rM)12 , where rSAr_{SA}rSA is the semi-annual rate and rMr_MrM is the monthly rate. Given a 7.8% semi-annual rate, or 0.078, we solve for rMr_MrM . Rearranging and solving gives an equivalent monthly rate of approximately 7.68%.